WORKING  DATA 

FOR 

IRRIGATION  ENGINEERS 


BY 

E.  A.  MORITZ,  B.S.C.E.;  C.E. 

Assoc.  M.  Amer.  Soc.  C.  E. 
Engineer  United  States  Reclamation  Service 


FIRST    EDITION 
FIRST  THOUSAND 


NEW  YORK 
JOHN  WILEY  &  SONS,  INC. 

LONDON:    CHAPMAN    &    HALL,    LIMITED 
1915 


Copyright,  1915,  by 
E.  A.  MORITZ 


PUBLISHERS  PRINTING  COMPANY 
207-217  West  Twenty-fifth  Street,  New  York 


PREFACE 

EVERY  branch  of  engineering  has  its  special  problems  which 
necessitate  the  frequent  use  of  certain  fundamental  data.  This 
requirement  has  led  to  the  production  of  " handbooks"  or 
"pocketbooks"  to  cover  the  requirements  of  the  various  fields 
and  the  following  pages  are  the  result  of  an  attempt  to  do  this 
for  irrigation  engineers.  The  object  has  been  to  produce  a  book 
that  would  result  in  the  conservation  of  the  time  and  mental 
energy  of  the  user,  as  well  as  to  present  material  not  readily 
obtainable  from  other  sources.  Utility  has  been  the  primary 
aim  in  the  selection  of  the  material  and  in  the  arrangement  of 
subjects. 

The  author  fully  realizes  that  he  has  accomplished  the  de- 
sired object  to  a  limited  extent  only.  The  first  edition  of  a 
work  of  this  nature  must  obviously  be  incomplete  in  numerous 
respects,  but  it  is  hoped  that  this  defect  may  be  remedied,  in 
large  part,  in  future  editions  if  such  should  become  necessary. 
To  accomplish  this,  constructive  criticisms  and  suggestions  for 
additions  and  improvements  are  earnestly  invited. 

A  considerable  portion  of  the  material  is  original.  Most  of 
the  remainder  was  taken  from  the  publications  and  records  of 
the  United  States  Reclamation  Service,  and  the  author  con- 
siders himself  very  fortunate  in  having  had  this  prolific  source  of 
valuable  information  at  his  disposal.  A  few  tables  of  a  general 
nature  were  collected  from  various  other  sources. 

It  is  hoped  that  the  book  in  its  present  form  will  prove  to  be 
of  value  to  irrigation  and  hydraulic  engineers,  and  the  author 
would  repeat  his  invitation  for  suggestions  for  its  improvement 
so  that  the  book  may  be  made  of  the  greatest  use  to  the  largest 
number. 

E.  A.  M. 
WASHINGTON,  D.  C., 
December,  1914. 


7W.TY-A4 


CONTENTS 

PAGE 

PREFACE .     .     .     .     .     .     .     .     .     .  iii 

LIST  OF  DIAGRAMS  ...     .     .     .     ... ix 

LIST  OF  TABLES xi 

INTRODUCTION xiii 

CHAPTER   I 

EXAMINATION  AND  RECONNOISSANCE 1 

Amount  of  Land  Available — Maps  Used — Source  of  Water  Supply 
and  Quantity  Available — Table  of  Water  Supply  Papers  Published 
by  the  Geological  Survey — Index  Map  of  Principal  Drainage  Basins 
in  the  United  States — Tables  of  Annual  Precipitation — Gaging 
Stations — Weir  Measurements — Current  Meter  Measurements — 
Prior  Water  Rights — Reservoirs  Available. 

CHAPTER   II 

INVESTIGATIONS  AND  SURVEYS      .     .     .     ; •.  .;     .....     20 

Water  Duty — Quantity  of  Water  Applied  to  Land — Monthly 
Variation  of  Use — Location  of  Point  of  Diversion — Location  of  Main 
Canal — Determination  of  Irrigable  Area — Reservoir  Surveys — 
General  Remarks  on  Canal  Location. 

CHAPTER   III 

DESIGN  OF  IRRIGATION  STRUCTURES 29 

Storage  Works — Evaporation  Tables — Seepage  from  Reservoirs — 
Types  of  Storage  Dams — Spillways — Maximum  Run-off  of  Streams — 
Outlet  Works — Diversion  Dams — Types  of  Diversion  Dams — Back- 
water Calculations — Discharge  Over  Diversion  Dams — Head- 
gates — Canals — Capacity — Seepage  Losses — Side  Slopes — Depth  of 
Flow — Bottom  Width — Velocities  and  Grades — Scouring  and  Silting 
Velocities — Formula  for  Flow  —  Kutter's  Coefficient  n  —  Free- 
board— Rise  of  Water  on  Curves — Chutes — Flumes — Pipes — Flow  of 
Water  in  Pipes — Tables  of  Discharge  of  Pipes — Vertical  Drops — 
Turnouts — Culverts. 

CHAPTER   IV 

HYDRAULIC  DIAGRAMS  AND  TABLES  ....;..    .     .     .     .     .     .     .     .     75 

Diagrams  for  Determining  Velocities  by  Kutter's  Formula — 
Table  of  Values  of  Coefficient  "C" — Hydraulic  Elements  of  Rec- 
tangular, Trapezoidal,  and  Circular  Sections — Hydraulic  Elements 
of  a  Horseshoe  Section — Discharge  and  Velocities  of  Circular  Conduits 


VI  CONTENTS 

PAGE 

Flowing  Partly  Full  by  Kutter's  Formula — Discharge  and  Velocity 
of  Rectangular  Wood  Flumes — Discharge  and  Velocity  of  Small 
Canals  in  Earth — Discharge  and  Velocity  of  Semicircular  Steel 
Flumes — Discharge  and  Velocity  of  Wood  Stave,  Cast-Iron,  Steel, 
and  Concrete  Pipe — Relative  Discharge,  Velocity,  and  Slope  for 
Different  Values  of  Kutter's  n — Velocity  Head  and  Total  Head 
Lost  for  Various  Coefficients  of  Discharge — Discharge  of  Sharp- 
Edged  Submerged  Orifices — Discharge  of  Sluice  Openings — Discharge 
of  Sharp-Edged  Cippoletti  Weirs — Discharge  of  Sharp-Edged  Con- 
tracted and  Suppressed  Weirs — Coefficients  for  Velocity  of  Approach 
for  Weirs — Coefficients  for  Submerged  Weirs — Ly man's  Table  of 
Discharges  of  Suppressed  Rectangular  Weirs — Discharge  of  Sup- 
pressed Rectangular  Weirs  by  Bazin's  Formula — Tables  of  Multi- 
pliers for  Broad-Crested  Weirs — Table  of  Acre-Feet  and  Second-Feet 
Equivalents — Water  Duty  Conversion  Diagram — List  of  Hydraulic 
Formulas. 

CHAPTER  V 

STRUCTURAL  DIAGRAMS  AND  TABLES 203 

Diagram  of  Excavation  and  Embankment  for  Small  Canals  in 
Level  Ground — Tables  of  Quantity  of  Material  in  Canal  Prisms  in 
Level  Ground  for  Various  Side  Slopes  and  Any  Bottom  Width — 
Tables  of  Quantity  of  Material  in  Canal  Prisms  in  Sloping  Ground 
for  Various  Side  Slopes  and  Any  Bottom  Width — Retaining  Walls 
and  Beams — Formulas  for  Maximum  Bending  Moments  in  Beams 
— Table  of  Bending  Moments  in  Beams — Formulas,  Diagram,  and 
Tables  for  Reinforced  Concrete  Design — Timber  Structures — Table 
of  Allowable  Unit  Stresses  and  Weight  of  Timber — Table  for  Pro- 
portioning Wooden  Beams — Table  of  Contents  in  Feet  B.  M.  of 
Lumber  of  Various  Sizes  and  Lengths — Table  of  Contents  in  Feet 
B.  M.  of  Logs  of  Different  Diameters  and  Lengths — Table  of  Spacings 
of  Bars  in  Concrete  Pressure  Pipe  and  Bands  on  Wood-Stave  Pipe — 
Diagram  of  Spacings  of  Bars  in  Concrete  Pressure  Pipe  and  Bands 
on  Wood  Stave-Pipe — Miscellaneous  Structural  Data  for  Wood  Pipe 
— Diagram  of  Thickness  of  Shell  of  Riveted  Steel  Pipe — Table  of 
Allowable  Depth  of  Backfill  Over  Steel  Pipe— Table  of  Thickness  and 
Weight  of  Cast-Iron  Pipe — Table  of  Dimensions  of  Steel  Flumes — 
Diagram  for  Converting  Head  of  Water  into  Pounds  per  Square  Inch 
— Diagram  for  Converting  Head  of  Water  into  Pounds  per  Square 
Foot — Diagram  of  Total  Hydrostatic  Pressure  on  a  Wall  One  Foot 
Wide  for  Different  Heads — Diagram  for  Converting  a  Given  Quantity 
of  Water  Falling  a  Given  Distance  into  Horse-Power. 


CHAPTER  VI 

MISCELLANEOUS  TABLES  AND  DATA        257 

Weights     of     Various     Substances — Convenient     Equivalents — 
Table  of  Inches  and  Fractions  Expressed   in  Decimals  of  a  Foot — 


CONTENTS  vii 

PAGE 

Metric  Conversion  Tables — Table  of  Corrections  in  Feet  for  Curva- 
ture and  Refraction — Stadia  Table — Trigonometric  Formulae — Curve 
Formulae — Common  Logarithms  of  Numbers — Natural  Sines,  Co- 
sines, Tangents,  and  Cotangents — Three-Halves  Powers  of  Num- 
bers— Conventional  Signs  for  Irrigation  Structures — Squares, 
Cubes,  Square  Roots,  Cube  Roots,  Reciprocals,  and  Areas  and 
Circumference  of  Circles. 


CHAPTER  VII 

SPECIFICATIONS 315 

Definition — Discussion — Subdivision  of  Specifications — The  Ad- 
vertisement— Notice  to  Bidders — The  Proposal — Guarantee  of 
Bond — Work  to  be  Performed — General  Conditions — Detail  Speci- 
fications— Special  Conditions — Canal  Excavation — Tunnels — Exca- 
vation for  Structures — Continuous  Wood-Stave  Pipe — Machine- 
Banded  Wood-Stave  Pipe — Steel  Pipe — Reinforced  Concrete  Pipe 
— Cast-Iron  Pipe — Metal  Flumes — Steel  Highway  Bridges — Con- 
crete— Paving — Cement — Timber  Piles — Structural  Steel  —  Steel 
Reinforcement  Bars — Gray  Iron  Castings — Malleable  Castings — 
Steel  Castings — Rolled  Bronze — Cast  Bronze. 

INDEX  .  .  389 


LIST  OF  DIAGRAMS 

FIG.  PAGE 

1.  Outline  Map  of  Drainage  Basins  in  the  United  States 5 

2.  Example  of  Discharge,  Mean  Velocity,  and  Area  Curves 18 

3.  Diagram  for  Use  in  Calculating  Seepage  Losses  in  Canals 45 

4.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .010 89 

5.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .012 91 

6.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .013 93 

7.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .014 95 

8.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .015 97 

9.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .020 99 

10.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .0225 101 

11.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .025 103 

12.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .030 105 

13.  Velocities,  Slopes,  and  Hydraulic  Radii  for  n  =  .035 107 

14.  Hydraulic  Elements  of  Rectangular  Sections Ill,  113,  115 

15.  Hydraulic  Elements  of  Trapezoidal  Sections,  Side  Slopes  ^£  to  1, 

117,  119,  121 

16.  Hydraulic  Elements  of  Trapezoidal  Sections,  Side  Slopes  1  to  1, 

123,  125,  127 

17.  Hydraulic  Elements  of  Trapezoidal  Sections,  Side  Slopes  1^  to  1, 

129,  131,  133 

18.  Hydraulic  Elements  of  Trapezoidal  Sections,  Side  Slopes  2  to  1, 

135,  137,  139 
19-20.  Hydraulic  Elements  of  Trapezoidal  Sections,  Mixed  Side  Slopes, 

141,  143 

19.  Hydraulic  Elements  of  Trapezoidal  Sections,  Side  Slopes  1  ^  to  1 ...    141 

20.  Hydraulic  Elements  of  Trapezoidal  Sections,  Side  Slopes  1%  to  1.  . .   143 

21.  Hydraulic  Elements  of  Circular  Segments 145,  147 

22.  Discharge  of  Circular  Conduits  Flowing  Full 151,  153 

23.  Discharge  of  Rectangular  Wooden  Flumes,  Slopes  .001  to  .01, 

154,  155,  156 

24.  Discharge  of  Rectangular  Wooden  Flumes,  Slopes  .01  to  .10, 

157,  158,  159 

25-26.  Hydraulic  Curves  for  Small  Canals  n  =  .0225 160,  165 

27-28.  Hydraulic  Curves  for  Small  Canals  n  =  .025 163,  165 

29.  Discharge  of  Semicircular  Steel  Flumes 167,  169 

30.  Flow  of  Water  in  Wood  Stave  Pipe 170,  171 

31.  Flow  of  Water  in  Cast  Iron  and  Monolithic  Concrete  Pipe 172,  173 

32.  Flow  of  Water  in  Riveted  Steel  and  Jointed  Concrete  Pipe 174,  175 

33.  Relative  Velocities  and  Slopes  for  Different  Values  of  n 176 

34.  Theoretical  Velocity  Head ' 177 

35.  Discharge  of  Sharp- Edged  Submerged  Orifices 178 

36.  Discharge  of  Standard  Cippoletti  Weirs 181 

37.  Discharge  of  Rectangular  Weirs 183 

ix 


X  LIST    OF    DIAGRAMS 

FIG.  PAGE 

38.  Diagram  for  Converting  "Acres  per  Second  Foot"  to  "Depth  of 

Water  Flowing  for  a  Given  Length  of  Time" 196 

39.  Volume  of  Excavation  and  Embankment  for  Small  Canals  in  Level 

Ground 205 

40.  Coefficients  of  Resistance  of  Reinforced  Concrete  Beams 229 

41.  Spacing  of  Bands  on  Wood  Stave  Pipe  and  Reinforcement  Rods  on 

Concrete  Pipe 243 

42.  Thickness  and  Weight  of  Steel  Pipe 245 

43.  Pressure  of  Water  in  Pounds  per  Square  Inch 250 

44.  Pressure  of  Water  in  Pounds  per  Square  Foot 251 

45.  Total  Hydrostatic  Pressure 252 

46.  Horse-Power  of  Falling  Water 253 


LIST  OF  TABLES 

PAGE 

1.  Numbers  of    Water-Supply  Papers  Containing  Results  of  Stream 

Measurements 2 

2-8.  Annual  Precipitation  in  Inches 6,  7,  8,  9,  10,  11,  12 

9.  Water  Used  on  Projects  of  U.  S.  Reclamation  Service 21 

10.  Water  Distribution  for  1912  U.  S.  Reclamation  Service 22 

11.  Total  Canal  Losses  in  Per  Cent  of    Diversions,  U.  S.  Reclamation 

Service 24 

12.  Evaporation  by  Months 30,  31,  32 

13.  Maximum  Rate  of  Discharge  of  Streams  in  the  United  States, 

34,  35,  36,  37 

14.  Seepage  Losses  from  Canals  in  Various  Materials 44 

15-16.  Critical  Velocity,  or  Mean  Velocity  at  which  a  Canal  Will  Neither 

Silt  Nor  Scour 49 

17.  Concrete    Channels — Values    of    Kutter's    Coefficient    n    from  Ex- 

periments   52,  53 

18.  Earth  Canals — Values  of  Kutter's  Coefficient  n  from  Experiments. 

54,  55,  56,  57,  58 


19. 

Flow  of  Water  in  Smooth  Straight  Iron  Pipes  by  Fanning's  Formula  . 

68 

20. 

Coefficients  of  Discharge  for  Submerged  Tubes  

84 

Values  of  "  C  "  for  n  =  .010  

88 

Values  of  "C"  for  n  =  .012  

90 

Values  of  "C"  for  n  =  .013  

92 

Values  of  "C"  for  n  =  .014  

94 

Values  of  "C"  for  n  =  .015  

96 

Values  of  "C"  for  n  =  .020  

98 

Values  of  "C"  for  n  =  .0225  

100 

Values  of  "C"  for  n  =  .025  

102 

Values  of  "C"  for  n  =  .030  

104 

Values  of  "C"  forn  =  .035.. 

106 

21.  Values  of  "C"  for  all  values  of  n 108,  109 

Hydraulic  Elements  of  Circular  Segments 146 

Hydraulic  Elements  of  a  Horseshoe  Section 149 

22.  Circular  Conduits  Flowing  Partly  Full 150,  152 

23.  Semicircular  Steel  Flumes — Freeboard,  Depth,  and  Area  for  Differ- 

ent Conditions  of  Flow 166 

24.  Semicircular  Steel  Flumes  Flowing  Partly  Full 168 

25.  Coefficients  for  Submerged  Weirs 180 

26.  Coefficients  for  Velocity  of  Approach  to  Weirs 182 

27.  Discharge  of  Suppressed  Rectangular  Weirs  for  Small  Heads 184 

28.  Discharge  of  Suppressed  Rectangular  Weirs  by  Bazin's  Formula ....  189 

28A.  Multipliers  of  Discharge  for  Broad-Crested  Weirs 192 

28B.  Multipliers  of  Discharge  for  Trapezoidal  Weirs 192 

28c.  Multipliers  of  Discharge  for  Compound  Weirs . 193 

xi 


Xll  LIST    OF    TABLES 

PAGE 

29.  Acre-Feet  Equivalent  to  a  Given  Number  of  Second-Feet 194,  195 

30.  List  of  Hydraulic  Formulas 197,  198,  199,  200 

31.  Amount  of  Material  in  Cubic  Yards  per  100  Linear  Feet  of  Level  Cut, 

Side  Slopes  1  to  1 208 

32.  Amount  of  Material  in  Cubic  Yards  per  100  Linear  Feet  of  Level  Cut, 

Side  Slopes  1^  to  1 209 

33.  Amount  of  Material  in  Cubic  Yards  per  100  Linear  Feet  of  Level  Cut, 

Side  Slopes  2  to  1 211 

34.  Amount  of  Material  in  Cubic  Yards  per  100  Linear  Feet  of  Level  Cut, 

Side  Slopes  3  to  1 212 

35.  Amount  of  Material  in  Cubic  Yards  per  100  Linear  Feet  of  Cut  on 

Sloping  Ground,  Side  Slopes  1  to  1 214 

36.  Amount  of  Material  in  Cubic  Yards  per  100  Linear  Feet  of  Cut  on 

Sloping  Ground,  Side  Slopes  1^  to  1 216 

37.  Amount  of  Material  in  Cubic  Yards  per  100  Linear  Feet  of  Cut  on 

Sloping  Ground,  Side  Slopes  2  to  1 218 

38.  Bending  Moments  in  Beams  with  Triangular  Loading 223,  224 

39.  Areas,  Weights,  and  Spacing  of  Round  Rods 230 

40.  Areas,  Weights,  and  Spacing  of  Square  Rods 231 

41.  Quantity  of  Material  Required  for  One  Cubic  Yard  of  Concrete ....  232 

42.  Allowable  Unit  Stresses  and  Weights  of  Timber 233 

43.  Values  of  M/S  for  Wooden  Beams 234 

44.  Contents  in  Feet  B.  M.  of  Lumber 235 

45.  Contents  in  Feet  B.  M.  of  Logs 236 

46.  Spacing  of  Rods  in  Concrete  and  Bands  on  Wood  Pipe, 

237,  238,  239,  240 

47.  Miscellaneous  Data  for  Wood  Pipe 242 

48.  Thickness  and  Weight  of  Cast-Iron  Pipe ...;.." 247,  248 

49.  Metal  Flumes,  Dimensions  and  Weights 249 

50.  Average  Weight,  in  Pounds  per  Cubic  Foot,  of  Various  Substances .  .  257 

51.  Convenient  Equivalents 258 

52.  Inches  and  Fractions  Expressed  in  Decimals  of  a  Foot 259 

53.  Comparison  of  Standard  Linear  Units 260 

54.  Meters  and  Millimeters  Converted  into  Feet  and  Inches 262,  263 

55.  Feet  and  Inches  Converted  into  Meters  and  Millimeters 264 

56.  Correction  in  Feet  for  Curvature  and  Refraction 265 

57.  Stadia  Table 266-272 

58.  Trigonometric  Formulae 273 

59.  Curve  Formulae 277 

60.  Common  Logarithms  of  Numbers 280 

61.  Natural  Sines  and  Cosines 282 

62.  Natural  Tangents  and  Cotangents 284 

63.  Three-Halves  Powers  of  Numbers 286 

64.  Conventional  Signs  for  Irrigation  Structures 291 

65.  Squares,  Cubes,  Square  Roots,  Cube  Roots,  Reciprocals,  and  Area 

and  Circumference  of  Circles .  .  .   292 


INTRODUCTION 

THE  major  portion  of  this  book  consists  of  tables  and  diagrams. 
Tables  are  given  generally  where  their  use  does  not  require  inter- 
polating for  intermediate  values;  for  example:  the  earthwork 
tables  on  pages  208  to  219,  where  the  arguments  of  the  tables  are 
given  as  close  as  the  measurements  are  made  in  the  field,  but  in 
most  other  cases  graphic  representation  has  been  preferred.  Dia- 
grams avoid  mental  interpolation;  they  throw  vividly  upon  the 
mind  a  picture  of  how  the  different  factors  vary.  Logarithmic 
scales  are  generally  used,  and  for  several  reasons:  First,  they 
allow  covering  the  greatest  range  of  values  in  a  given  amount 
of  space;  second,  on  these  scales,  most  of  the  curves  are  straight 
or  nearly  so,  making  the  reading  of  the  diagram  easier  than 
where  the  lines  are  curved,  as  on  natural  scales;  third,  from 
whatever  part  of  the  diagram  a  value  is  read,  the  same  degree 
of  accuracy  is  obtained,  which  is  not  the  case  when  natural  scales 
are  used.  Most  hydraulic  calculations  do  not  warrant  the 
high  degree  of  refinement  generally  indicated  in  tables,  which 
is  liable  to  be  misleading,  especially  to  the  inexperienced.  The 
diagrams  give  results  that  are  well  within  the  limit  of  accuracy 
of  the  data,  and,  at  the  same  time,  avoid  the  implication  of  an 
accuracy  that  does  not  exist. 

It  seems  desirable,  before  entering  on  a  detailed  explanation 
of  the  tables  and  diagrams,  to  discuss  briefly  the  various  features 
of  irrigation  engineering,  in  order  to  show  more  completely  the 
applicability  of  the  matter  that  follows.  To  this  end,  the  usual 
steps  in  the  development  of  an  irrigation  project  are  taken  up 
in  the  order  of  their  sequence,  and  data  are  presented  that  are 
of  assistance  in  arriving  at  the  proper  conclusions. 

In  discussing  the  various  features,  irrigation  by  gravity  from 
surface  waters  is  kept  principally  in  mind,  as  this  is  by  far  the 
most  important  method,  but  most  of  the  principles  apply  to 
irrigation  by  pumping  as  well;  the  main  difference  being  that 
the  latter  method  generally  presents  a  much  simpler  problem 
in  the  aggregate. 

xiii 


WORKING    DATA    FOR   IRRIGATION 
ENGINEERS 

CHAPTER  I 
EXAMINATION  AND   RECONNOISSANCE 

Amount  of  Land  Available. — The  amount  of  land  available 
is  generally  much  greater  than  the  available  water  supply  will 
cover,  but  a  reconnoissance  is  always  desirable  to  determine  its 
location,  both  horizontally  and  in  elevation,  relative  to  the 
source  of  supply.  From  this  is  determined  the  probable  length 
of  the  main  supply  canal,  and  it  can  be  roughly  judged  whether 
the  amount  of  land  to  be  irrigated  will  warrant  the  construction 
of  a  main  supply  canal  of  the  length  found.  The  topographic 
sheets  of  the  U.  S.  Geological  Survey  are  exceedingly  valuable 
for  this  purpose,  and  if  such  sheets  are  available  for  the  territory 
under  investigation,  very  little  examination  in  the  field  will 
usually  be  necessary.  Index  maps,  showing  the  topographic 
sheets  available,  and  for  sale  at  10  cents  each,  may  be  obtained 
upon  application  to  the  U.  S.  Geological  Survey.  If  such  sheets 
are  not  available,  a  reconnoissance  with  hand  level,  aneroid 
barometer,  and  pocket  compass  will  generally  be  necessary. 
For  reference  in  establishing  elevations,  the  "Dictionary  of 
Altitudes"  and  pamphlets  giving  the  results  of  spirit-levelling 
in  the  various  States,  published  by  the  U.  S.  Geological  Survey, 
are  very  useful.  These  may  be  obtained  by  application  to  the 
Director,  U.  S.  Geological  Survey,  Washington,  D.  C. 

Source  of  Water  Supply  and  Quantity  Available. — The  flow 
of  rivers  comes  from  two  general  sources :  rain  and  melting  snow. 
Either  of  these  is  likely  to  produce  sudden  and  large  floods, 
but  those  produced  by  the  former  are,  as  a  rule,  much  more 
sudden  and  violent,  and  the  rivers  in  arid  regions  fed  principally 
by  rains  often  go  dry,  or  almost  dry,  during  the  summer  months, 
such  as  the  Arkansas  River,  in  Colorado  and  Kansas,  and  the 

1 


FOR  IRRIGATION  ENGINEERS 


CQ 


vo     «o     t-   oo 

CM       CM       CM     CM 


IO       to        t-     OO     OS       OrH       CM 
O        O        OOO        iHrH        rH 

co     co     coeoeo     coco     co 


00    OS     O»-I»-H        CM 

oo    oo    ososos      os 

CM     CM     CMCMCM       CM 


Ot-tTH       CM 
CM 


us     «o     t-   oo   os   Oi-ii-i 

TJ«        TJ<       T)<     r}<     TJ<     10  10  10 
CM       CM       N    <N    N    CMCMCM 


CMC 


rHCMCO     CO^     iO  to       t-       00    IO  OS  O    iH     CM  CO  CO       rf 
000     00     00         O         O     OOi-l     ^H     1-lrHiH         »H 


»OCOt-     t-00    OSO       T-l       CM     oj  CO  Tl«  10  t- tO  t- t-     t-00 

tototo   toto   tot-     t-     t-   <gt-t-t-t-i>t~t-    t-t- 
-«<uv^s~,  Cl    *        O      «t       ^i 


koto   tot-   ooos   ooooJoOOi-iM   eo   CO^TI<     10 

C\JCM  CM  CM  CM  CM  CM  CO  CO  ;4  CM  CO  CO  CO  CO  CO  CO   CO 


t-  00       OOt-     OSO     OS       OS     OS     O       00       O 

0>  OS       OS  OS     '^,-1     OS       OS     OS     O       00       O 


o     coco     10     •««•     Tf^m     uiio     m 
o     oooo     oq     oo     oqoooo     oooo     oo 


00  00       OSOS       OS       O       OOO       i-l    r-t       T-I 

"*  rf       rJ«Tlt       Tf       IO       IOIO1O       IOIO       1O 

V»  rfi  -» 


gj  I 

!! 


rt  :   I   1 1  a 

PQ   :     P4     .20^     ' 


1  -2  I 

pq    e     fi. 


o   o  o 


S  § 

42  "-» 

!  1 

"3  -I 


"3         S 

i  si  4]  1 1 

8  |g  ?.!  i 


-U      011 

O     g  C     WJ     LJ 


I  a 


lljlljll 

:  2  o  •*,  &-.S  >*  «o  *>- 


.S      O 


s5     Si 


v.«        re  (y 

*  *•§  rt  -I  S 

4  4"  I  Jl  § 

o-     ft'S     rt  3  S  ^ 

^  f I  5  "Sc  ^ 

5  2^    g 

rtrtCJ      jj  gti(               f 

>    S.S    -g  3.3  "B 

S    Bg    =  sf  |i 

I II II  &  II 


*i 


05 


EXAMINATION  AND   RECONNOISSANCE 

Milk  River,  in  Montana.  Rivers  fed  by  melting  snows  are 
much  more  reliable  as  an  irrigation  supply,  but  even  these  often 
run  very  low  during  the  summer  months. 

On  account  of  this  variable  and  flashy  nature  of  streams  in 
the  arid  regions,  it  is  of  the  utmost  importance  that  records  be 
obtained  not  only  of  the  total  flow  of  the  stream,  but  also  of 
the  monthly  run-off,  especially  during  the  irrigation  season. 
For  this  purpose,  the  records  of  the  Hydrographic  Branch  of 
the  U.  S.  Geological  Survey  are  of  great  value.  Thorough  search 
for  records  from  private  sources  should  also  be  made.  The 
Geological  Survey  records  are  published  in  various  water-supply 
papers,  a  general  index  of  the  data  available  to  date  being  given 
in  the  accompanying  table. 

I.  North  Atlantic  Coast. — Includes  streams  flowing  into  the  Atlantic  Ocean  from  St.  John 
River  in  Maine,  to  Rappahannock  River,  Va.,  inclusive.    Principal  streams  in  this  division: 
St.  Croix,   Machias,  Union,  Penobscot,  Kennebec,  Androscoggin,  Saco,  Merrimac,  Mystic, 
Blackstone,   Connecticut,   Hudson,   Delaware,   Susquehanna,   Potomac,  and   Rappahannock. 
The  streams  drain  wholly  or  in  part,  the  States  of  Connecticut,  Delaware,  Maine,  Maryland, 
Massachusetts,  New  Jersey,  New  Hampshire,  New  York,  Pennsylvania,  Rhode  Island,  Ver- 
mont, Virginia,  and  West  Virginia. 

II.  South  Atlantic  Coast  and  Eastern  Gulf  of  Mexico. — Includes  streams  flowing  into  the 
Atlantic  Ocean  and    Gulf  of  Mexico  from  James  River,  Va.,  to  Pearl  River,  Miss.,  inclusive. 
Principal  streams  in  this  division:    James,  Roanoke,  Cape  Fear,  Yadkin,  Santee,  Savannah, 
Altamaha,  Apalachicola,  Choctawhatchee,  Mobile,  and  Pearl.    The  streams  drain  wholly  or 
in  part  the  following  States:   Alabama,  Florida,  Georgia,  Mississippi,  North  Carolina,  South 
Carolina,  and  Virginia. 

III.  Ohio  River  Basin. — Includes  Ohio  River  with  all  its  tributaries.    Principal  streams: 
Allegheny,  Monongahela,  Beaver,  Muskingum,  New  (or  Kanawha),  Scioto,  Miami,  Kentucky, 
Wabash,  Cumberland,  and  Tennessee.     The  streams  drain  wholly  or  in  part  the  following 
States:   Alabama,  Georgia,  Illinois,  Indiana,  Kentucky,  Mississippi,  New  York,  North  Caro- 
lina, Ohio,  Pennsylvania,  Tennessee,  Virginia,  and  West  Virginia. 

IV.  St.  Lawrence  River  Basin. — Includes  streams  which  drain  into  the  Great  Lakes  and 
St.  Lawrence  River.     Principal  minor  basins:    Lake  Superior,  Lake  Michigan,  Lake  Huron, 
Lake  Erie,  Lake  Ontario,  and  St.  Lawrence  River.    Principal  streams  flowing  into  Lake  Su- 
perior:  St.  Louis,  Ontbnagon,  Dead,  and  Carp  Rivers.    Streams  flowing  into  Lake  Michigan 
are  Escanaba,  Menominee,  Iron,  Peshtigo,  Oconto,  Fox,  St.  Joseph,  and  Grand  Rivers.    Streams 
flowing  into  Lake  Huron  are  Thunder  Bay,  Au  Sable,  Rifle,  and  Flint  Rivers.    Streams  flowing 
into  Lake  Erie  are  Huron,  St.  Marys,  Maumee,  Sandusky,  Black,  and  Cuyahoga.     Streams 
flowing  into  Lake  Ontario  are  Genesee,  Oswego,  Salmon,  and  Black  Rivers.     Streams  flowing 
into  the  St.  Lawrence  are  Oswegatchie,  Raquette,  Richelieu  (the  outlet  of  Lake  Champlain), 
and  St.  Francis    River,  whose    principal    tributary,  Clyde    River,  reaches    it    through  Lake 
Memphremagog.     The  streams  of  this  section  drain  wholly  or  in  part  the  following  States: 
Illinois,    Indiana,    Michigan,    Minnesota,    New   York,    Ohio,    Pennsylvania,   Vermont,   and 
Wisconsin. 

V.  Hudson  Bay  and  Upper  Mississippi  River  Basins. — Include  all  streams  which  drain 
into  Hudson  Bay  and  the  Mississippi  above  its  junction  with  the  Ohio  (except  the  Missouri). 
The  principal  streams  flowing  into  Hudson  Bay  from  the  United  States  are  St.  Mary  River, 
Red  River,  and  Rainy  River.     The  principal  tributaries  of  the  upper  Mississippi  are  Crow 
Wing,  Sauk,  Crow,  Rum,  Minnesota,  St.  Croix,  Chippewa,  Zumbro,  Black,  Root,  Wisconsin, 
Wapsipinicon,  Rock,  Iowa,  Des  Moines,  Illinois,  Fox,  and  Kaskaskia  Rivers.     The  streams 
drain  wholly  or  in  part  the  following  States:    Illinois,  Indiana,  Iowa,  Minnesota,  Missouri, 
North  Dakota,  South  Dakota,  and  Wisconsin. 


4  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

VI.  Missouri  River  Basin. — Includes  the  Missouri  with  all  its  tributaries.    The  principal 
streams  in  this  basin  are  Red  Rock,  Beaverhead,  and  Jefferson  Rivers,  which  may  be  con- 
sidered a  continuous  river  forming  the  head  of  the  Missouri;  below  the  mouth  of  the  Jefferson 
the  principal  tributaries  are  Madison,  Gallatin,  Prickly  Pear,  Little  Prickly  Pear,  Dearborn, 
Sun,  Marias,  Judith,  Musselshell,  Milk,  Yellowstone,  Little  Muddy,  Little  Missouri,  Cheyenne, 
Niobrara,  and  Platte  (including  North  Platte  and  South  Platte  Rivers),  Kansas,  Osage,  and 
Gasconade  Rivers.     These  streams  drain  wholly  or  in  part  the  following  States:     Colorado, 
Iowa,  Kansas,  Minnesota,  Missouri,   Montana,  Nebraska,  North  Dakota,   South  Dakota, 
and  Wyoming. 

VII.  Lower  Mississippi  River  Basin. — Includes  all  streams  flowing  into  the  Mississippi 
below  the  mouth  of  the  Ohio.     The  principal  streams  in  this  division  are  Meramec,  White, 
Arkansas   (whose  chief    tributaries   are  Huerfano,  Purgatory,  Cimarron,  Verdigris,  Neosho, 
Canadian,  and  Mora  Rivers),  Yazoo,  Homochitto,  and  Red  Rivers.    The  streams  drain  wholly 
or  in  part  the  following  States:  Arkansas,  Colorado,  Kansas,  Kentucky,  Louisiana,  Mississippi, 
Missouri,  New  Mexico,  Oklahoma,  Tennessee,  and  Texas. 

VIII.  Western  Gulf  of  Mexico  Drainage  Basins. — Include  all  streams  draining  into  the 
western  Gulf  of  Mexico  and  into  the  Rio  Grande.     Principal  streams  flowing  into  the  Gulf 
of  Mexico  above  the  mouth  of  the  Rio  Grande:    Sabine,  Trinity,  Brazos,  Colorado  River  of 
Texas,  and  Guadalupe.    Principal  tributaries  of  the  Rio  Grande  are  Rio  Hondo,  Rio  Puerco, 
Pecos,  and  Rio  San  Juan.    The  streams  drain  wholly  or  in  part  the  following  States:  Colorado, 
Louisiana,  Mexico,  New  Mexico,  and  Texas. 

IX.  Colorado  River  Basin. — Includes  the  Colorado  and  its  tributaries,  of  which  the  most 
important  are  Green  River  (considered  the  continuation  of  the  Colorado),  Grand  River,  Do- 
lores, San  Juan,  Little  Colorado,  Virgin,  and  Gila  Rivers.    The  principal  streams  flowing  into 
the  Green  are  Newfork,  Yampa,  Ashley  Creek,  White  River,  Duchesne,  Lake  Fork,  and 
Uinta.    The  principal  tributaries  of  Grand  River  are  Grand  Lake,  Frazer  River,  Williams  Fork, 
Blue  River,  and  Gunnison  River.    The  streams  of  the  Colorado  basin  drain  wholly  or  in  part 
the  following  States:  Arizona,  California,  Colorado,  Nevada,  New  Mexico,  Utah,  and  Wyoming. 

X.  Great  Basin. — Includes  streams  which  do  not  discharge  into  the  ocean.     The  basin 
is  made  up  of  a  number  of  minor  basins,  of  which  the  most  important  are  Great  Salt  Lake, 
Sevier  Lake,  Humboldt  Sink,  and  Truckee,  Walker,  Carson,  and  Owens  River,  and  Honey, 
Mono,  Malheur,  Harney,  Warner,  Abert,  Summer,  Silver,  and  Goose  Lake  basins.      The 
streams  of  this  section  drain  wholly  or  in  part  the  following  States:   California,  Idaho,  Nevada, 
Oregon,  and  Utah. 

XI.  California. — Includes    rivers    draining    into    the    Pacific    Ocean    from    California. 
Principal  streams:    Tia  Juana,  Sweetwater,  San  Diego,  Bernardo,  San  Luis  Rey,  and  Los 
Angeles  Rivers;  San  Joaquin  River,  whose  principal  tributaries  are  Kern,  Kings,  Merced, 
Tuolumne,  and  Stanislaus  Rivers;  Sacramento  River,  whose  principal  tributaries  are  Pit, 
Feather,  and  American;  and  the  following  streams  flowing  into  the  Pacific  Ocean  above  San 
Francisco  Bay:    Russian,  Eel,  Mad,  and  Klamath  Rivers.    With  the  exception  of  the  Kla- 
math  River,  which  receives  a  drainage  from  a  small  area  in  Oregon,  all  the  streams  in  this 
division  are  entirely  in  California. 

XII.  North  Pacific  Coast. — Includes  streams  flowing  into  the  Pacific  Ocean  from  Oregon 
and  Washington.     Most  important  of  these  are  Rogue,  Umpqua,  and  Columbia  Rivers  and 
streams  flowing  into  Puget  Sound.      The  principal  tributaries  of  the  Columbia  are  Clark 
Fork,  Kootenai,  Spokane,  Wenatchee,  Yakima,  Snake,  Bruneau,  Boise,  Walla  Walla,  Uma- 
tilla,  John  Day,  Deschute,  Hood,  and  Willamette  Rivers.    The  following  streams  flow  into 
Puget  Sound:    Nisqually,  Puyallup,  White,  Snoqualmie,  and  Skagit.     The  streams  of  this 
division  drain  wholly  or  in  part  the  following  States:    Idaho,  Montana,  Nevada,  Oregon, 
Utah,  Washington,  and  Wyoming. 


The  accompanying  map  shows  the  outlines  of  the  above- 
described  drainage  basins. 

The  engineer  is  fortunate,  indeed,  if  he  can  find  monthly  run- 
off records  for  a  number  of  years.  When  such  records  are  not 
available  it  often  happens  that  isolated  measurements  have  been 
made  which  will  give  some  idea  of  the  run-off.  If  no  measure- 


EXAMINATION  AND  RECONNOISSANCE 


f 


6 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


TABLE   2 

ANNUAL  PRECIPITATION,  IN  INCHES.    NORTH  PACIFIC  STATES  AND  NORTH- 
ERN ROCKY  MOUNTAIN  PLATEAU 


1 

j 

§ 

£ 

£ 

* 

tfl 

4 

4 

i 

c 

Year 

8 

§ 

3 

6 

1 

0 

§ 

1 

i 

11 

1 

g 

•§ 

a 

X 

g 

2 

•g 

a 

oJ 
9 

*j 

jj 

«j 

1 

I 
1 

I 

.0 

I 

| 

'1 

1 

5 

w 

"3 

11 

| 

c 

£ 

1872  

6.03 

10.10 

17.93 

46.90 

20.24 

21.40 

1873    .  .  . 

5.90 

13.58 

17.74 

50  52 

21.94 

21.90 

1874      . 

9  73 

9.58 

14.97 

46.17 

20.11 

22.40 

1875  

23.64 

9.58 

12.44 

13.76 

60.08 

23.90 

23.47 

1876  

21.28 

5.67 

16.15 

..... 

11.12 

54.94 





... 

25.83 

25.12 

1877  

16.35 

6.47 

12.91 



13.80 

58.30 





25.57 

27.88 

1878  

19.75 

6.77 

26.78 

36.92 

10.21 

47.70 

63.34 

30.21 

28.05 

1879  

13.11 

9.36 

16.32 

45.03 

17.63 

62.22 

73.44 

33.87 

28.43 

1880  

10.94 

6.13 

12.01 

31.44 

10.66 

51.87 

62.77 

12.18 

24.75 

28.49 

1881  

16.88 

11.91 

9.87 

43.68 

13.56 

58.05 

65.56 

22.68 

19.94 

15.54 

27.77 

26.54 

1882  

15.98 

10.46 

14.97 

34.77 

14.43 

67.24 

51.59 

25.99 

10.32 

12.76 

25.85 

24.70 

1883  

14.24 

8.40 

11.01 

22.48 

15.27 

51.45 

41.61 

14.37 

10.55 

15.10 

20.45 

24.01 

1884  

17.52 

18.38 

21.38 

29.19 

21.05 

38.31 

35.58 

20.56 

19.18 

25.67 

24.68 

22.73 

1885  

19.69 

11.80 

18.37 

30.91 

12.56 

39.59 

41.95 

19.01 

10.99 

8.37 

21.32 

22.54 

1886  

18.89 

8.16 

12.02 

35.17 

12.23 

38.76 

48.13 

15.86 

12.63 

11.48 

21.33 

22.83 

1887  

11.66 

8.05 

11.91 

37.34 

11.34 

54.17 

61.78 

20.10 

14.05 

18.94 

24.93 

21.86 

1888  

13.62 

4.89 

23.94 

31.19 

11.09 

38.76 

45.54 

17.69 

10.14 

21.87 

21.50 

1889  

18.46 

5.75 

39.26 

28.12 

10.95 

31.76 

33.75 

14.27 

6.71 

9.40 

19.84 

22.64 

1890  

10.33 

11.27 

14.60 

34.65 

12.53 

40.29 

35.70 

16.57 

8.80 

10.37 

19.51 

22.38 

1891 

15.92 

9.68 

23.04 

46.90 

13.31 

47.41 

58.73 

16.69 

19.39 

19.41 

27.05 

23.10 

1892 

14.08 

7.85 

46.26 

28.88 

11.75 

33.58 

49.41 

16.78 

15.27 

12.40 

23.63 

24.06 

1893  

17.35 

7.85 

26.46 

37.86 

13.87 

39.03 

61.62 

22.00 

15.48 

13.31 

25.48 

24.04 

1894  

15.27 

10.12 

20.92 

44.29 

14.12 

39.32 

58.57 

17.84 

11.17 

14.49 

24.61 

23.34 

1895  

11.95 

6.84 

25.55 

29.92 

7.90 

30.76 

46.60 

13.46 

10.69 

10.94 

19.41 

24.56 

1896  

18.42 

11.08 

27.68 

43.69 

22.95 

44.13 

65.46 

20.32 

15.38 

16.48 

28.56 

23.38 

1897  

16.74 

6.66 

17.40 

34.83 

16.98 

43.01 

58.50 

23.84 

16.16 

13.30 

24.74 

23.68 

1898  

16.09 

7.08 

8.54 

25.93 

33.90 

42.22 

13.08 

17.40 

12.11 

19.59 

24.18 

1899  

17.57 

8.47 

23.15 

42.97 

14.81 

42.21 

62.22 

20.08 

11.78 

17.88 

26.11 

23.10 

1900  

11.53 

7.43 

21.17 

29.74 

12.77 

38.22 

56.37 

18.72 

11.62 

11.43 

21.90 

23.29 

1901  

16.08 

8.73 

20.76 

34.37 

9.59 

41.05 

55.08 

15.99 

14.71 

15.03 

23.14 

23.71 

1902  

11.41 

4.99 

25.65 

39.58 

12.15 

50.15 

70.77 

19.23 

10.09 

12.94 

25.70 

23.50 

1903  

14.62 

6.53 

20.26 

29.50 

9.55 

35.62 

56.88 

16.55 

11.36 

16.03 

21.69 

22.83 

1904  

16.31 

9.44 

29.51 

43.42 

14.08 

46.37 

61.67 

13.97 

7.49 

8.61 

25.09 

23.46 

1905  

14.23 

6.42 

19.67 

21.14 

9.77 

34.10 

46.43 

16.68 

10.08 

6.76 

18.52 

23.21 

1906  

21.28 

10.50 

33.68 

30.21 

14.19 

43.29 

63.86 

17.60 

14.28 

14.13 

26.30 

22.90 

1907  

19.22 

11.35 

17.73 

42.12 

15.92 

42.89 

51.68 

17.69 

12.74 

13.28 

24.46 

22.30 

Mean.  . 

23.89 

ments  whatever  are  available,  the  best  that  can  be  done  as  a 
preliminary  step  is  to  measure  the  slope  and  cross-section  of  the 
stream  and  calculate  the  probable  maximum  run-off,  and  com- 
pare the  drainage  basin  with  others  of  known  run-off  by  means 
of  rainfall  records  which  may  be  obtained  from  the  publications 
of  the  U.  S.  Weather  Bureau.  Tables  2  to  8  compiled  by  the 


EXAMINATION  AND  RECONNOISSANCE  7 

TABLE   3 
'ANNUAL  PRECIPITATION,  IN  INCHES.     NORTHERN  ROCKY  MOUNTAIN  SLOPE 


,& 

. 

J 

i 

1 

5 

j  . 

a 

j.C 

QQ- 

i 

1 

Year 

g 

d 

3 

1 

s 

1 

| 

M 

o 

§2 

it 

§•§ 

* 

i 

9 

| 

1 

c 

1 

S"i 

13 

f! 

|| 

l« 

V 
V 

•a 

3 
| 

1 

2 

Q 

1 

o 

£i 

PQ 

Sj 

0.03 

SI 

II 

J3 
U 

1 

E 

1872  

18.05 

32.48 

19.42 

14.86 

16.80 

13.48 

19.17 

17.80 

1873 

11.81 

27.04 

14.62 

13.19 

27.39 

20.76 

10.01 

17.83 

18.00 

1874 

13.46 

25.75 

16.24 

12.64 

27.63 

7.58 

9.71 

16.14 

18.22 

1875 

10.78 

17.25 

15.35 

42.89 

13.99 

27.52 

13.53 

19.59 

14.85 

12.10 

18.79 

18.91 

1876  

15.40 

20.12 

11.84 

32.51 

19.54 

30.92 

25.75 

18.13 

12.34 

5.03 

19.16 

19.90 

1877  

27.89 

16.38 

25.47 

40.95 

22.92 

17.68 

21.67 

29.38 

12.29 

11.71 

22.63 

20.45 

1878  

17.96 

15.51 

18.62 

37.05 

20.19 

20.23 

33.83 

35.72 

16.11 

12.64 

22.79 

20.63 

1879  

15.43 

10.86 

20.06 

30.31!  23.50 

22.61 

19.31 

19.76 

19.67 

7.34 

18.89 

21.22 

1880  

18.12 

9.58 

17.48 

28.52   16.66 

19.75 

27.35 

27.60 

13.25 

8.38 

19.67 

20.59 

1881  

33.55 

12.78 

22.93 

45.74 

14.85 

15.76 

19.26 

29.48 

14.90 

11.88 

22.11 

20.74 

1882  

13.14 

14.49 

17.95 

37.68 

12.20 

21.33 

22.48 

34.01 

12.73 

8.64 

19.47 

21.26 

1883  

28.50 

19.49 

30.01 

48.92 

19.91 

15.66 

17.88 

24.96 

10.82 

19.24 

23.54 

21.39 

1884  

30.36 

15.07 

13.53 

47.68 

11.97 

23.36 

21.81 

28.50 

7.37 

15.54 

21.52 

20.49 

1885 

23.71 

15.95 

22.03 

36.68 

20.82 

13.08 

17.37 

22.68 

15.56 

15.11 

20.30 

20.06 

1886 

19.35 

15.07 

13.10 

22.67 

16.00 

13.26 

29.24 

26.76 

10.24 

10.36 

17.61 

18.73 

1887 

15.71 

12.49 

21.68 

19.92 

14.26 

16.33 

23.36 

21.97 

15.43 

11.82 

17.30 

17.54 

1888  

22.94 

9.51 

17.46 

24.22 

14.77 

16.51 

17.99 

16.50 

14.70 

14.51 

16.91 

16.68 

1889  

19.17 

14.75 

20.66 

22.97 

15.29 

11.03 

11.75 

17.07 

8.46 

14.65 

15.58 

17.83 

1890  

11.72 

9.33 

12.71 

22.08 

13.28 

16.75 

23.50 

21.79 

14.24 

14.47 

15.99 

18.16 

1891  

32.34 

21.43 

23.36 

34.92 

13.18 

20.50 

25.93 

24.31 

18.98 

18.97 

23.39 

17.88 

1892 

19.66 

15.02 

20.37 

29.44 

18.81 

18.17 

16.34 

24.94 

14.26 

13.50 

18.95 

17.81 

1893  

10.12 

8.48 

13.16 

26.66 

14.56 

13.74 

20.07 

23.58 

15.45 

9.22 

15.50 

18.14 

1894 

12.60 

15.09 

11.21 

17.82 

7.82 

14.32 

20.29 

22.43 

17.76 

12.98 

15.23 

17.63 

1895  

20.31 

16.12 

14.58 

21.69 

16.85 

16.92 

20.60 

17.38 

17.07 

14.76 

17.63 

17.48 

1896  

19.87 

11.84 

16.52 

35.90 

17.35 

16.64 

26.80 

22.04 

20.79 

20.86 

17.91 

1897 

21.58 

15.37 

17.09 

21.30'  18.84 

14.33 

25.80 

12.19 

17.25 

18.19 

18.42 

1898.  .  . 

31.46 

12.98 

15.54 

28.84 

10.65 

13.67 

19.83 

14.44 

13.05 

17.66 

18.78 

1899     . 

28.45 

9.33 

13.99 

26.74 

20.00 

15.47 

16.01 

20.64 

12.61 

14.18 

17.74 

18.20 

1900  

20.76 

15.29 

12.29 

31.20 

16.81 

17.88 

21.06 

27.50 

15.81 

16.09 

19.47 

18.66 

1901  

16.06 

9.10 

16.44 

25.08 

17.04 

15.59 

16.50 

30.16 

18.36 

14.99 

17.93 

[19.01 

1902  

17.70 

13.35 

26.27  30.48 

20.04 

15.95 

18.97 

29.12 

16.85 

16.50 

20.52 

19.10 

1903  

15.27 

9.50 

18.36 

33.43 

19.53 

17.96 

21.64 

28.29 

17.69 

12.25 

19.39 

19.64 

1904  

17.19 

14.05 

23.17 

25.48 

9.15 

14.17 

27.81 

26.36 

9.44 

15.72 

18.21 

20.70 

1905  

25.96 

17.68 

26.81 

29.88 

20.46 

17.19 

18.70 

31.48 

10.66 

22.68 

22.15 

19.93 

1906  

32.54 

16.84 

27.99 

27.59 

22.06 

18.22 

21.21 

26.00 

22.01 

17.65 

23.21 

19.40 

1907  

18.26 

11.83 

19.61 

24.60 

14.02 

16.55 

16.31 

23.02 

10.18 

12.34 

16.67 

18.80 

Mean 

19.11 

Weather  Bureau  contain  valuable  general  information  in  regard 
to  rainfall.  If  the  project  has  any  considerable  size  or  impor- 
tance, nothing  short  of  monthly  run-off  records  for  a  series  of 
years  will  justify  its  construction.  This  is  fully  borne  out  by 
the  numerous  failures  of  irrigation  schemes  because  of  insufficient 
water  and  other  cases  where  failure  was  avoided  only  by  the 
construction  of  expensive  storage  works. 


8  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

TABLE   4 
ANNUAL  PRECIPITATION,  IN  INCHES.    LAKE  REGION  AND  CENTRAL  VALLEYS 


I 

, 

i 

d 

| 

| 

d 

1 

Year 

.y 

O 

. 

.2 

23 

i 

~ 

jfl 

.5 

• 

s 

s 

•o 

'rt 

I 

a 

it 

a 
•3 

""^ 

2 

^ 

8 

H 

ri 
I 

1 

| 

g 
1 

i 

1 

• 

8 

*r* 

1 

3 
*3 

3 

1 

^ 

U 

U 

c 

g 

a 

Q 

U 

55 

Q 

* 

S 

1872. 

34.39 

34.68 

34.12 

26.52 

30.47 

29.07 

29.72 

25.63 

30.58 

36.95 

1873  

31.10 

41.33 

41.38 

52.83 

50.86 

45.50 

36.41 

34.75 

34.32 

40.96 

37.50 

1874  

25.18 

33.39 

37.45 

43.92 

47.58 

37.88 

28.63 

35.51 

26.43 

35.11 

38.34 

1875  

37.27 

36.91 

42.58 

54.58 

52.93 

43.00 

38.06 

30.66 

35.71 

41.30 

39.64 

1876.'.... 

37.62 

41.19 

52.62 

57.56 

55.60 

48.46 

36.48 

23.67 

40.40 

43.73 

39.51 

1877  

41.00 

33.13 

34.65 

39.08 

39.47 

41.43 

41.01 

28.80 

35.23 

37.09 

40.09 

1878  

38.48 

53.51 

41.62 

38.62 

41.76 

40.83 



41.95 

22.78 

43.39 

40.33 

40.28 

1879  

39.97 

41.52 

51.60 

42.88 

45.41 

25.70 

32.82 

30.71 

32.39 

37.17 

38.02 

40.17 

1880  

43.63 

37.38 

54.67 

50.99 

49.56 

34.66 

36.66 

37.32 

29.76 

47.68 

42.23 

41.51 

1881  

45.61 

34.96 

47.24 

48.74 

32.18 

37.37 

56.81 

44.18 

39.16 

45.44 

43.17 

41.85 

1882  

45.10 

39.98 

52.12 

53.68 

61.58 

43.15 

47.60 

41.34 

23.14 

30.32 

43.80 

41.66 

1883  

85.32 

41.13 

52.35 

54.12 

52.54 

40.10 

39.69 

45.86 

26.70 

32.57 

42.04 

40.38 

1884  

35.53 

33.26 

39.28 

39.99 

51.66 

40.64 

41.14 

34.61 

26.11 

28.17 

37.04 

38.28 

1885  

34.71 

39.93 

33.94 

39.51 

31.99 

45.59 

35.03 

44.37 

25.33 

28.24 

35.06 

35.77 

1886 

40.12 

27.34 

31.35 

39.88 

37.98 

44.34 

29.53 

26.77 

22.89 

26.71 

32.69 

34.12 

1887 

37.88 

35.36 

35.08 

33.08 

26.75 

35.30 

24.60 

29.13 

25.85 

28.97 

31.20 

32.77 

1888 

29.36 

32.57 

34.88 

41.36 

41.90 

41.17 

31.15 

30.86 

25.86 

29.02 

33.81 

33.31 

1889  

31.32 

32.57 

30.92 

38.41 

37.74 

33.16 

25.90 

34.95 

16.96 

21.06 

30.30 

33.17 

1890 

31.35 

47.82 

47.70 

54.87 

50.53 

37.63 

24.74 

32.69 

23.38 

34.99 

38.57 

34.24 

1891  

31.61 

34.18 

38.44 

38.23 

39.56 

30.53 

30.14 

26.54 

21.74 

28.83 

31.98 

34.51 

1892  

32.15 

36.51 

31.95 

39.77 

38.71 

41.62 

38.42 

36.56 

32.55 

37.11 

36.54 

35.92 

1893  

33.35 

33.88 

44.00 

39.35 

48.79 

39.33 

25.64 

27.47 

25.95 

34.18 

35.19 

31.90 

1894  

30.88 

27.73 

26.59 

31.13 

30.51 

27.44 

20.06 

27.46 

25.80 

25.74 

27.33 

32.28 

1895  

21.59 

26.84 

29.33 

33.54 

33.57 

31.20 

26.80 

32.38 

24.26 

25.04 

28.46 

32.20 

1896  

30.14 

36.68 

34.48 

39.84 

39.36 

37.55 

37.09 

33.14 

34.73 

36.20 

35.89 

32.55 

1897  

32.59 

24.54 

43.89 

42.15 

44.10 

40.17 

27.07 

25.85 

30.51 

30.34 

34.12 

33.28 

1898  

34.07 

32.54 

38.97 

44.10 

48.66 

49.20 

28.33 

33.77 

25.34 

34.34 

36.93 

33.88 

1899  

29.93 

24.53 

34.69 

36.87 

42.42 

34.61 

26.73 

26.49 

27.54 

26.41 

31.02 

32.05 

1900  

23.03 

25.83 

27.78 

38.45 

36.89 

29.51 

38.46 

28.65 

34.22 

31.45 

31.43 

32.47 

1901  

25.23 

38.71 

17.99 

30.33 

31.68 

24.80 

19.77 

24.52 

25.75 

28.78 

26.76 

31.77 

1902  

29.02 

39.89 

37.30 

37.70 

33.07 

38.43 

42.01 

37.57 

31.75 

35.53 

36.23 

31.90 

1903  

31.54 

35.41 

34.69 

32.46 

32.91 

33.81 

31.43 

28.09 

37.88 

35.88 

33.41 

32.53 

1904  

24.68 

34  .  56 

29.54 

45.42 

32.00 

33.71 

28.43 

26.14 

34.11 

28.32 

31.69 

34.27 

1905  

28.14 

31.90 

38.69 

33.29 

39.48 

38.54 

37.50 

35.36 

30.76 

32.00 

34.56 

34.03 

1906  

35.22 

31.62 

40.83 

37.47 

46.92 

35.52 

29.44 

30.87 

33.21 

33.67 

35.48 

33.70 

1907  

22.68 

34.76 

44.56 

38.56 

45.58 

41.39 

34.02 

35.10 

23.07 

30.62 

35.03 

33.20 

Mean 

35.55 

In  case  good  records  are  not  available,  and  the  project  appears 
from  other  considerations  to  be  a  feasible  one,  measuring  stations 
should  be  established  and  rain  gages  installed  at  convenient 
points  on  the  irrigable  area  and  drainage  basin.  If  the  stream  is 
a  very  small  one,  a  weir  may  be  used  for  measuring  the  flow,  but  if 
this  is  not  possible,  a  current  meter  station  should  be  established. 
In  either  case,  a  reliable  local  resident  should  be  employed  to 


EXAMINATION  AND  RECONNOISSANCE 
TABLE   5 

ANNUAL  PRECIPITATION,  IN  INCHES.     NORTH  ATLANTIC  STATES 
AND  NEW  ENGLAND 


U 

V 

i 

I 

\ 

> 

^ 

d 

4 

Q' 

1 

I 

Year 

3 

c 

0 

3 

M 

z 

£ 

OH 

1 

1 

I 

S 

S 

B 

g 

c 

> 

>; 

4 

3 

1 

«fl 

.S 

£ 

i 

S 

1 

3 
PQ 

2 

8 

PQ 

E 
z 

I 

1 

PQ 

S 

1 

1 

I 

1 

3 
C 
C 

1 

S 

1872  

32.25 

50.62 

45.78 

31.25 

31.91 

48.36 

30.86 

56.95 

41.00 

41.90 

1873  

25.92 

54.53 

39.98 



44.63 

41.42 

55.28 

45.70 

55.43 

45.36 

41.97 

1874  

42.56 

31.94 

43.52 

39.84 

37.93 

30.44 

39.42 

46.25 

34.58 

50.41 

39.69 

42.05 

1875  

45.42 

26.94 

50.15 

45.19 

38.25 

31.44 

34.05 

40.22 

41.11 

50.97 

40.37 

42.66 

1876  

57.99 

27.53 

48.96 

47.40 

38.19 

29.26 

37.01 

47.39 

47.96 

46.54 

43.82 

43.58 

1877  

50.62 

33.17 

51.49 

40.94 

36.09 

34.48 

34.72 

37.26 

52.59 

69.13 

44.05 

42.87 

1878  

51.37 

41.45 

65.53 

46.66 

49.37 

60.24 

38.76 

34.53 

60.09 

51.87 

49.99 

42.20 

1879  

43.48 

24.27 

45.67 

36.21 

38.66 

30.47 

37.02 

36.75 

32.83 

35.88 

36.12 

41.28 

1880  

42.44 

25.21 

37.30 

37.34 

32.54 

39.26 

31.97 

33.58 

38.83 

51.84 

37.03 

40.86 

1881  

55.98 

20.99 

52.63 

40.40 

36.34 

35.95 

37.30 

30.21 

42.20 

40.06 

39.21 

39.47 

1882  

47.18 

25.64 

43.82 

46.61 

33.76 

33.82 

38.63 

45.58 

46.79 

57.67 

41.95 

41.20 

1883  

53.17 

35.48 

38.83 

39.37 

38.07 

43.17 

39.17 

45.71 

54.30 

43.03 

42.13 

1884  

64.53 

33.37 

49.18 

55.34 

38.90 

37.07 

34.82 

39.34 

49.96 

45.05 

44.76 

42.85 

1885  

54.06 

33.64 

45.10 

42.12 

34.39 

52.36 

34.12 

33.35 

44.84 

43.25 

41.72 

42.39 

1886.  . 

28.47 

42.14 

46.73 

34.01 

44.85 

39.21 

37.24 

58.17 

54.33 

42.79 

42.79 

1887  

46.96 

31.13 

33.75 

46.63 

39.70 

31.55 

41.95 

42.17 

35.08 

47.74 

39.67 

43.49 

1888  

53.25 

33.97 

45.89 

52.95 

44.66 

33.87 

39.89 

44.06 

45.05 

56.64 

45.02 

44.14 

1889  

42.26 

38.21 

39.82 

58.68 

39.51 

40.07 

41.37 

50.60 

61.33 

70.72 

48.26 

43.57 

1890  

45.02 

38.51 

45.93 

52.30 

44.89 

46.55 

50.61 

34.02 

41.59 

50.22 

44.96 

43.43 

1891  

36.44 

39.12 

39.70 

41.44 

41.68 

30.74 

38.28 

38.19 

52.95 

50.63 

39.92 

42.39 

1892 

32.20 

42.24 

37.02 

38.90 

34.83 

45.87 

32.66 

34.78 

42.34 

49.24 

39.01 

39.80 

1893  

29.87 

29.04 

41.84 

53.01 

35!39 

38.64 

37^84 

37.65 

36.71 

57.90 

39.79 

37^56 

1894  

22.84 

22.96 

36.62 

44.17 

35.11 

38.92 

28.17 

40.34 

30.85 

53.09 

35.31 

35.82 

1895  

32.88 

28.69 

40.17 

35.73 

29.80 

32.02 

27.50 

31.01 

34.25 

45.41 

33.75 

36.24 

1896  

31.54 

28.38 

37.55 

37.99 

27.88 

37.29 

44.35 

32.15 

31.16 

44.22 

31.25 

36.68 

1897  

39.57 

43.44 

40.77 

44.27 

40.79 

37.72 

35.08 

42.04 

44.58 

42.66 

41.09 

36.92 

1898  

45.16 

31.78 

49.86 

45.12 

38.77 

33.50 

35.76 

49.23 

37.72 

53.14 

42.00 

37.79 

1899  

36.44 

37.25 

34.69 

42.06 

28.92 

29.39 

33.85 

39.96 

44.02 

38.41 

36.50 

39.90 

1900  

47.35 

34.24 

44.05 

41.78 

30.56 

35.93 

25.73 

40.91 

41.20 

39.34 

38.11 

39.65 

1901  

41.61 

33.88 

48.72 

47.06 

40.53 

35.49 

40.76 

45.54 

41.75 

42.61 

41.80 

39.29 

1902  

41.41 

38.36 

33.93 

47.07 

37.48 

32.91 

32.22 

49.76 

46.58 

38.48 

39.82 

39.47 

1903  

36.67 

32.86 

41.97 

48.60 

34.09 

37.95 

38.81 

41.50 

43.55 

46.10 

40.21 

39.38 

1904  

38.89 

29.71 

39.64 

41.57 

31.26 

35.83 

33.76 

39.76 

40.84 

42.  6C 

37.39 

39.08 

1905  

31.88 

34.73 

32.08 

44.48 

26.98 

35.85 

35.19 

41.61 

50.64 

43.29 

37.67 

38.97 

1906  

39.49 

29.87 

40.69 

41.82 

32.51 

33.63 

31.29 

51.87 

52.92 

49.23 

40.33 

38.40 

1907  

44.42 

29.67 

37.56 

45.28 

33.63 

34.97 

34.86 

48.74 

44.66 

38.72 

39.25 

38.10 

Mean 

40.61 

read  the  gage  daily,  recording  the  readings  on  suitable  blanks 
furnished  for  the  purpose,  or  a  recording  gage  may  be  estab- 
lished which  will  give  a  continuous  record  of  the  height  of  water 
in  the  form  of  a  diagram. 

The  rain  gage  consists  of  a  metal  cylinder  having  a  funnel- 
shaped  top  leading  to  a  smaller  cylinder  inside  having  a  cross- 


10  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

TABLE   6 
ANNUAL  PRECIPITATION,  IN  INCHES.     EAST  GULP  STATES 


Year 

Hatteras,  N.  C. 

Charleston,  S.  C. 

Jacksonville,  Fla. 

Key  West,  Fla. 

New  Orleans,  La. 

Galveston,  Tex. 

Montgomery,  Ala. 

Augusta,  Ga. 

Memphis  Tenn. 

Fort  Smith,  Ark. 

1 

1 

a 

< 

Five-year  means 

1872 

57.06 
62.15 
62.51 
50.97 
78.42 
78.11 
77.44 
50.29 
46.69 
43.20 
57.01 
51.35 
60.22 
67.93 
35.94 
44.69 
49.46 
52.15 
47.84 
45.50 
53.32 
70.99 
57.81 
55.18 
47.78 
56.65 
46.42 
44.33 
38.10 
32.70 
37.22 
42.86 
37.88 
34.85 
43.62 
31.71 

57.17 
60.65 
48.31 
57.60 
55.28 
50.58 
60.42 
47.18 
65.51 
54.69 
53.26 
53.34 
55.02 
82.00 
54.86 
58.60 
53.13 
46.22 
47.52 
41.34 
41.89 
58.23 
56.84 
46.80 
40.19 
60.70 
45.71 
38.57 
53.85 
54.22 
55.52 
52.03 
49.17 
55.77 
46.86 
45.07 

31.77 
32.75 
32.75 
36.35 
37.95 
38.15 
49.03 
58.54 
33.41 
53.10 
41.86 
48.24 
33.05 
34.03 
30.13 
43.62 
35.58 
52.67 
42.87 
39.75 
24.91 
22.00 
42.34 
29.19 
25.72 
46.46 
43.39 
29.55 
48.81 
37.02 
38.61 
30.36 
37.98 
41.84 
48.53 
26.65 

60.68 
65.55 
62.74 
85.73 
67.25 
63.09 
66.16 
51.27 
69.83 
64.01 
50.18 
69.85 
60.01 
64.18 
54.83 
64.97 
83.13 
48.45 
42.17 
38.62 
56.91 
48.02 
54.44 
56.44 
49.68 
43.47 
49.00 
31.07 
56.33 
57.73 
41.61 
57.18 
43.69 
80.07 
41.59 
66.32 

41.72 
58.91 
49.39 
58.48 
50.92 
66.87 
60.90 
26.93 
50.97 
53.28 
57.68 
41.11 
62.98 
62.56 
40.97 
43.43 
65.88 
37.52 
47.80 
41.51 
24.78 
35.43 
40.64 
38.91 
23.71 
29.24 
42.00 
41.76 
78.39 
51.33 
37.67 
52.47 
42.65 
48.60 
31.16 
43.93 

55.17 
64.00  48.50 
51.93  57.19 
58.16   54.68 
59.74  46.16 
50.26   53.97 
55.40  46.34 
48.46  40.99 
54.22  47.91 
53.81   54.77 
54.75  49.62 
39.71  39.90 
48.61  45.10 
58.89  40.67 
56.25  46.04 
44.74  45.09 
61.39  49.88 
45.62  49.25 
48.18  42.98 
51.05  47.76 
69.85  39.27 
47.481  48.  91 
41.35  55.54 
43.45   52.10 
45.  82'  43.  45 
46.25  51.83 
39.75  43.99 
50.63  48.74 
59.92  51.22 
52.24  50.94 
48.62  41.79 
48.99  51.83 
37.00  29.54 
47.23  40.92 
50.13  53.91 
49.83  38.93 

43.95 
56.20 
45.71 
57.02 
55.49 
73.50 
49.34 
52.29 
61.67 
42.84 
71.05 
57.14 
64.69 
37.41 
57.72 
42.52 
46.82 
44.67 
68.28 
51.31 
61.46 
44.45 
54.52 
38.59 
35.00 
46.03 
48.58 
38.99 
47.42 
34.58 
50.32 
36.17 
42.56 
55.85 
54.31 
41.55 

49.65 
56.09 
51.32 
58.58 
57.44 
64.06 
60.25 
49.63 
58.09 
53.17 
55.67 
52.43 
54.67 
54.73 
46.58 
48.14 
55.40 
49.60 
50.78 
45.68 
47.46 
47.85 
50.15 
47.98 
48.23 
47.54 
45.82 
42.58 
51.87 
44.36 
42.66 
45.62 
39.28 
48.93 
46.66 
42.41 

50.04 

53.25 
53.60 
54.62 
57.50 
58.33 
57.99 
57.89 
57.04 
55.36 
53.80 
54.81 
54.13 
53.84 
5F.33 
51.92 
50.91 
50.12 
49.92 
49.78 
48.27 
48.38 
47.82 
46.33 
46.25 
45.94 
44.43 
45.21 
46.43 
45.46 
45.42 
44.76 
44.17 
44.63 
44.58 
44.55 
44.40 

1873  

1874  

1875  

68.26 
65.78 
102.04 
77.18 
70.72 
92.64 
58.81 
66.60 
76.96 
66.41 
68.02 
54.72 
55.07 
56.73 
67.24 
55.51 
59.50 
52.88 
58.30 
57.85 
69.28 
45.25 
58.82 
48.20 
61.88 
45.65 
50.11 
40.13 
48.87 
40.97 
41.66 
53.94 
44.56 

1876  
1877  
1878  
1879  
1880  
1881  
1882  
1883  
1884  
1885 



50^63 
31.61 
35.33 
38.69 
50.97 
43.20 
64.63 
40.49 
49.35 
44.70 
41.21 
49.87 
25.70 
41.91 
51.12 
40.27 
39.05 
22.77 
35.12 
35.46 
31.39 
42.50 
42.50 
35.58 

1886  

1887  

1888  

1889  

1890  
1891  
1892  
1893  
1894  
1895  . 

1896  
1897  
1898  
1899  
1900  
1901  
1902  
1903  
1904  
1905  
1906  
1907  

Mean  .  . 

sectional  area  of  one-tenth  that  of  the  larger  cylinder,  so  that 
the  depths  of  water  accumulated  in  the  smaller  cylinder  magnify 
the  actual  precipitation  ten  times,  and  thus  enable  very  small 
rainfalls  to  be  accurately  measured.  The  water  depth  in  the 
small  cylinder  is  measured  at  the  end  of  each  rain  by  a  cedar 
stick  graduated  to  inches  and  tenths  of  inches.  Standard 
rain  gages  are  generally  furnished  by  the  Weather  Bureau 


EXAMINATION  AND   RECONNOISSANCE 
TABLE   7 


11 


ANNUAL  PRECIPITATION,  IN  INCHES.     WEST  GULF  STATES  AND  SOUTHERN 
ROCKY  MOUNTAIN  SLOPE 


1 

^ 

.   t 

. 

jj 

t 

& 

. 

1 

•^8 

£H 

jfj 

JJ 

J 

3J 

1 

| 

B 
j 

Year 

"5 

0 

itf 

«*o- 

o 

S 

I 

1 

1 

M 

I 

a 

c 

*fl 

III" 

jfa 

3 

C/3 

rt 

1 

1 
* 

2 

I 

| 

£ 

c 

g.5  <S 

i|| 

If 

ft 

9 

c 

t: 

o 

tj 

o 

| 

| 

1 

$ 

Otf£ 

£<: 

1 

w 

£ 

3 

i 

(6 

1 

£ 

1872.  .  . 

26.17 

46.49 

20.58 

25.14 

9.87 

13.61 

7.68 

14.76 

21.67 

20.78 

21.20 

1873  .  .  . 

34.02 

52.68 

12.03 



33.80 

9.73 

11.62 

5.77 

19.63 

26.66 

22.88 

21.80 

1874 

41.55 

43  .06 

26  .34 

28.89 

19.93 

20.38 

7.24 

20.33 

26.85 

26.  06 

22.33 

1875.'.'. 

21^95 

36.93 

18.76 



37^39 

18.97 

19.66 

6^48 

11.94 

18.36 

21.16 

23!  33 

1876 

39.32 

19.71 

24.42 

15.07 

18.94 

9.46 

13.26 

25.81 

20.75 

24.35 

1877. 

30.29 

31  .89 

36.61 

43.11 

13.15 

13.  12 

12.53 

25.86 

25.82 

22.87 

1878.'.'. 

39.60 

31.41 

29.77 



25.55 

19.52 

18.92 

22.53 

36.35 

27.96 

23.44 

1879... 

22.80 

18.93 

20.86 

11.44 

13.77 

6.81 

19.94 

34.73 

18.66 

24.45 

1880.  .. 

41.91 

28.71 

16.79 

33.75 

9.89 

16.90 

14.37 

15.77 

38.07 

24.02 

24.38 

1881.  .  . 

26.  78  ;  36  .00 

20.86 

16.16 

28.22 

30.82 

18.17 

23.40 

31.74 

25.79 

23.91 

1882.  .  . 

36.39:57.20 

21.76 

24.76 

31.13 

11.37 

19.27 

8.27 

11.95 

32.56 

25.47 

26.62 

1883. 

43.49 

21  .76 

28.21 

12.92 

16.16 

31.02 

25.59 

27.17 

1884 

51.64 

35.86 

33.91 

18.30 

12.77 

40.91 

32.23 

26.63 

1885.  .. 

32.92 

41.85 

21.37 

37.07 

33.05 

14.89 

7.31 

20.64 

31^83 

26.77 

26.83 

1886  .  .  . 

26.22 

33.21 

19.14 

23.05 

19.57 

15.90 

11.84 

8.06 

14.01 

60.06 

23.11 

27.15 

1887... 

20.13 

38.04 

24.63 

22.83 

34.17 

13.38 

12.39 

6.76 

32.27 

59.87 

26.45 

25.45 

1888... 

40.55 

59.66 

30.58 

16.51 

35.72 

12.03 

13.07 

9.79 

21.32 

32.58 

27.18 

25.13 

1889  .  .  . 

38.96 

46.43 

25.23 

19.40 

29.29 

7.89 

6.59 

7.10 

21.67 

34.61 

23.72 

23.85 

1890.  .  . 

29.79 

52.06 

28.50 

15.41 

31.08 

12.88 

15.86 

8.49 

13.43 

25.55 

20.20 

23.24 

1891.  .  . 

30.04 

45.27 

17.57 

17.15 

32.76 

16.79 

10.30 

2.22 

16.60 

28.25 

21.70 

21.39 

1892.  .  . 

25.81 

61.19 

28.48 

15.60 

34.32 

11.62 

8.80 

5.32 

19.25 

23.38 

20.62 

1893  .  .  . 

18.24 

30.58 

16.27 

17.23 

24.19 

14.94 

15.47 

10.88 

17.51 

14!  36 

17.97 

21.46 

1894... 

21.75 

46.05 

24.39 

15.81 

24.14 

13.31 

8.67 

4.24 

21.80 

18.33 

19.85 

21.41 

1895... 

26.07 

43.72 

35.30 

24.79 

29.17 

20.24 

14.45 

10.20 

21.11 

19.20 

24.42 

20.98 

1896... 

34.09 

38.40 

20.74 

24.28 

17.12 

14.28 

18.85 

9.79 

17.10 

19.41 

21.41 

21.47 

1897... 

15.92 

39.48 

23.30 

19.16 

26.29 

20.40 

18.00 

12.41 

19.19 

18.14 

21.23 

22.09 

1898.  .  . 

22.49 

42.05 

22.13 

22.54 

37.56 

12.97 

16.21 

6.16 

9.75 

12.31 

20.42 

22.23 

1899.  .  . 

19.65 

47.71 

23.41 

27.39 

46.51 

10.05 

10.78 

7.30 

17.48 

19.50 

22.98 

21.53 

1900.  .  . 

37.19 

44.32 

32.11 

24.40 

36.47 

15.89 

12.61 

7.95 

14.99 

25.10 

21.76 

1901... 

16.44 

41.22 

15.71 

24.42 

16.07 

17.41 

8.94 

8.68 

11.32 

19.20 

17.94 

22:13 

1902... 

24.79 

39.76 

27.05 

23.11 

46.79 

13.36 

15.67 

10.15 

5.28 

17.62 

22.36 

22.  14 

1903... 

33.11 

39.48 

26.53 

20.28 

18.68 

9.79 

12.33 

11.63 

22.85 

26.78 

22.15 

23.34 

1904  .  .  . 

29.38 

32.37 

17.80 

21.33 

30.32 

14.19 

11.30 

28.55 

23.10 

23.15 

24.84 

1905.  .  . 

32.59 

46.30 

33.06 

32.32 

50.08 

17.22 

17.80 

20.98 

29.35 

31.08 

24.56 

1906... 

20.42 

32.94 

29.05 

24.92 

38.78 

16.60 



14.99 



26.12 

25.48 

23.70 

1907... 

27.77 

38.01 

18.33 

18.09 



15.15 



8.41 





20.96 

22.80 

Mean 

23  50 

1  

free  of  cost,  provided   the  records  are  regularly  supplied  to 
the  bureau. 

The  weir  station  is  applicable  only  to  very  small  streams. 
Three  standard  types  of  weirs  are  used  for  measuring  water: 
(1)  The  Cippoletti  weir,  having  the  sides  inclined  on  a  slope  of 
one  horizontal  to  four  vertical.  (2)  The  contracted  rectangular 


]2  WORKING  DATA   FOR   IRRIGATION  ENGINEERS 

TABLE   8 

ANNUAL  PRECIPITATION,  IN  INCHES.     SOUTHERN  PACIFIC  STATES  AND 
SOUTHERN  ROCKY  MOUNTAIN  PLATEAU 


3 

01 

Year 

.3 

i 

I 

i 

1 

3 

1 

O 

3 

U 

I 

§ 

£ 

1" 

1 

1 

| 

u 

1 

1 

1 

I 

1 

1 

1 

1 

S 

1 

K 

IS 
o 

1 

V 

3 

1 

§ 

E 

1872  

16.66 

4.11 

4.41 

26.48 

22.45 

10.33 

35.03 

6.07 

15.69 

14.00 

1873  



12.14 

2.75 

5.04 

19.38 

18.55 

10.00 

26.81 

13.01 

13.46 

14.40 

1874  

5.70 

4.47 

24.34 

22.52 

7.76 

33.02 

10.93 

15.53 

14.47 

1875...". 

6.06 

4.62 

15.41 

22.63 

12.65 

33.99 

6.80 

14.59 

13.29 

1876  

0.94 

16.16 

14.02 

3.59 

4.93 

21.86 

23.54 

7.10 

31.65 

7.24 

13.10 

14.03 

1877  

3.66 

11.09 

12.77 

5.68 

4.52 

17.54 

11.93 

4.30 

18.07 

8.12 

9.77 

14.19 

1878.  . 

2.88 

15.63 

16.66 

6.32 

6.56 

31.16 

33.26 

10.43 

34.94 

13.87 

17.17 

14.10 

1879  

3.29 

12.89 

12.01 

4.02 

7.12 

25.05 

30.76 

8.44 

45.14 

14.71 

16.34 

14.12 

1880  

0.74 

10.02 

6.61 

6.70 

3.85 

17.38 

30.07 

13.81 

41.68 

10.37 

14.12 

14.87 

1881  

0.98 

15.45 

14.92 

5.89 

7.13 

15.53 

20.73 

8.02 

35.54 

5.00 

13.22 

13.66 

1882  

1.78 

15.26 

15.59 

5.48 

9.14 

17.69 

18.67 

9.03 

32.84 

9.74 

13.52 

14.88 

1883  

3.96 

16.13 

8.50 

3.95 

7.08 

16.00 

15.43 

10.18 

21.61 

8.01 

11.09 

14.35 

1884  

5.86 

26.75 

15.03 

6.17 

4.94 

23.19 

38.82 

23.79 

52.41 

27.59 

22.46 

14.28 

1885  

2.72 

10.11 

5.26 

2.95 

6.23 

2.0.41 

24.90 

9.89 

26.31 

5.73 

11.45 

14.02 

1886 

5,35 

18.78 

8.63 

4.82 

2.64 

15.91 

20.02 

7.83 

29.41 

15.35 

12.87 

14.37 

1887 

3.90 

17.36 

12.95 

5.78 

3.25 

15.44 

19.04 

6.45 

27.77 

10.45 

12.24 

13.67 

1888  .  .  . 

2.95 

18.52 

10.60 

4.60 

2.00 

19.91 

23.03 

10.55 

24.79 

11.57 

12.85 

14.57 

1889 

4.69 

20.83 

18.37 

6.56 

4.21 

29.82 

36.94 

12.78 

38.97 

16.03 

18.92 

14.55 

1890 

4.67 

21.17 

15.04 

6.36 

11.85 

21.78 

25.43 

11.54 

34.04 

8.02 

15.99 

15.31 

1891  

2.67 

14.66 

7.30 

10.45 

7.62 

19.79 

21.11 

8.56 

26.52 

8.99 

12.77 

15.46 

1892 

3.35 

12.90 

11.25 

11.92 

3.78 

36.24 

22.08 

10.03 

39.56 

9.09 

16.02 

14.71 

1893  

3.00 

14.01 

13.26 

4.74 

3.47 

25.49 

17.91 

9.07 

34.77 

10.29 

13.60 

14.17 

1894 

2.95 

11.97 

7.41 

7.27 

3.85 

30.61 

24.32 

15.50 

43.49 

4.35 

15.17 

15.15 

1895  

1.33 

14.50 

11.07 

5.55 

4.53 

27.35 

17.13 

8.36 

31.95 

11.33 

13.31 

14.73 

1896  

2.55 

16.23 

11.39 

10.59 

6.14 

33.78 

28.25 

14.22 

44.76 

8.73 

17.66 

13.78 

1897  

4.18 

21.88 

10.77 

8.00 

6.19 

20.84 

16.40 

8.80 

32.94 

8.93 

13.89 

13.60 

1898  

2.38 

11.89 

12.72 

5.81 

3.99 

12.31 

9.31 

5.69 

19.96 

4.67 

8.87 

13.39 

1899  

0.60 

10.91 

8.38 

8.29 

4.10 

27.30 

23.23 

11.75 

41.86 

6.08 

14.25 

12.77 

1900  

0.85 

10.33 

7.79 

15.17 

6.25 

20.14 

15.33 

11.09 

30.22 

5.77 

12.29 

12.25 

1901  

3.65 

12.97 

9.72 

11.36 

8.24 

20.27 

19.75 

9.30 

40.53 

9.49 

14.53 

13.11 

1902  

1.93 

14.31 

8.60 

4.94 

4.19 

28.04 

19.18 

9.17 

11.49 

11.32 

13.58 

1903  

0.98 

16.74 

8.80 

6.55 

4.46 

22.76 

18.33 

11.03 

35.82 

6.09 

13.16 

14.59 

1904  

1.43 

15.86 

7.85 

10.63 

8.27 

30.39 

24.72 

12.84 

47.55 

6.61 

16.62 

15.98 

1905  

11.41 

39.47 

24.17 

5.69 

2.37 

24.11 

16.24 

9.18 

24.20 

16.36 

17.32 

17.14 

1906  

5.40 

25.13 

11.75 

11.05 

3.92 

37.27 

26.34 

19.65 

60.63 

14.90 

21.50 

17.20 

1907  

2.61 

20.80 

14.09 

11.27 

4.95 

24.15 

22.47 

15.23 

47.26 

7.95 

17.08 

16.00 

Mean 

14  55 

weir,  having  the  sides  vertical;  and,  (3)  The  suppressed  rectan- 
gular weir  having  the  sides  vertical  and  flush  with  the  sides  of 
the  approach  channel.  The  discharge  of  the  Cippoletti  weir  is 
given  by  the  formula  Q  =  3.37  L  JET3/2  values  of  which  are 
given  in  Fig.  36.  The  discharge  of  contracted  rectangular  weirs 
is  given  by  the  formula  Q  =  3.33  (L  -  .2H)  H  V*  values  of 


EXAMINATION  AND   RECONNOISSANCE  13 

which  are  given  in  Fig.  37.  Neither  of  these  formulas  considers 
velocity  of  approach,  and  in  order  to  make  them  accurate  there 
should  be  a  pool  of  comparatively  still  water  just  above  the 
weir.  If  a  pool  does  not  exist  and  is  impossible  of  construction, 
the  measured  head  must  be  corrected  for  velocity  head  when 
the  velocity  of  approach  is  greater  than  0.5  to  1  foot  per  second. 
The  formulas. for  both  Gippoletti  and  contracted  rectangular 
weirs  give  discharges  that  are  too  large  when  the  head  on  the 
crest  is  greater  than  one-third  the  crest  length,  and  the  error 
increases  as  the  head  increases  beyond  this  ratio,  being  about 
30  per  cent  for  a  ratio  of  head  to  crest  length  of  1.  If  correc- 
tion for  velocity  of  approach  is  necessary  these  weirs  generally 
become  undesirable  as  measuring  devices  and  the  suppressed  weir 
is  much  better.  Bazin's  formula  for  this  weir  automatically 
corrects  for  velocity  of  approach  and  a  direct  measurement  of 
the  head  and  height  of  weir  above  approach  channel  is  all  that 
is  necessary,  no  matter  what  the  velocity  of  approach  is.  One 
fundamental  requirement,  however,  must  be  met  before  this 
can  be  accomplished,  namely,  that  the  approach  channel  be  of 
uniform  cross-section  for  some  distance  above  the  weir.  To 
this  end  it  is  usually  necessary  to  construct  an  artificial  channel 
which  should  be  capable  of  being  cleaned  of  silt  and  debris 
when  necessary. 

The  proper  location  and  operation  of  a  current-meter  station 
is  a  larger  subject  than  can  be  comprehensively  discussed  here, 
but  a  few  general  points  will  be  considered.  The  station  should 
be  located  in  a  straight  and  uniform  stretch  of  the  stream,  and 
where  the  water  is  confined  between  the  banks  of  the  normal 
channel  at  all  stages.  The  gage  should  be  located  out  of  the 
path  of  all  disturbing  elements  and  be  of  such  range  as  to  cover 
all  stages  of  the  river  from  the  lowest  to  the  highest.  Measure- 
ments are  made  by  wading,  from  a  convenient  bridge,  or  from 
a  cable  car  established  for  the  purpose.  The  first  method  can 
obviously  be  used  only  in  shallow  streams.  If  a  bridge  is  located 
across  a  section  of  the  river  complying  with  the  general  require- 
ments for  a  current-meter  station,  thegagings  can  be  conveniently 
made  therefrom,  and  the  cost  of  constructing  and  maintaining  a 
cable  station  need  not  be  incurred. 


14  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

For  gagings  by  wading,  the  measuring  points  may  be 
located  by  rags  tied  to  a  wire  stretched  across  the  stream.  In 
measurements  from  a  bridge,  the  points  may  be  located  by  marks 
painted  on  the  floor  beam  or  lower  chord  of  the  bridge.  At 
cable  stations  the  points  are  located  on  the  cable  by  any  con- 
venient means.  In  all  cases  the  measuring  points  should  be 
permanently  fixed. 

The  current  meter  consists  essentially  of  a  wheel  which  is 
caused  to  rotate  by  the  currents  of  the  flowing  water,  and  a 
device  for  determining  the  number  of  revolutions  of  the  wheel. 
Each  meter  should  be  rated  before  it  is  used,  to  determine  the 
relation  between  revolutions  of  the  wheel  and  velocity  of  the 
water.  In  rating  the  meter  it  is  driven  at  different  uniform 
speeds  through  still  water  for  a  given  distance,  and  the  number 
of  revolutions  counted.  The  relation  of  velocity  of  water  to 
revolutions  of  the  wheels  is  for  all  meters  practically  a  linear  one, 
that  is,  if  60  revolutions  per  minute  correspond  to  a  velocity  of 
1  foot  per  second,  120  revolutions  per  minute  correspond  to  2 
feet  per  second,  etc.  Velocities  less  than  0.3  foot  per  second  can 
not  be  measured  with  a  current  meter,  as  it  requires  a  certain 
small  velocity  to  overcome  the  inertia  of  the  wheel  and  start  it 
revolving.  Many  kinds  of  current  meters  have  been  constructed, 
but  the  Price  meter,  manufactured  by  W.  and  L.  E.  Gurley, 
Troy,  N.  Y.,  is  probably  best  adapted  for  general  use.  These 
meters  are  made  in  two  general  styles — one  with  an  electric  de- 
vice for  indicating  the  revolutions  to  the  ear,  and  the  other  with 
a  direct  acoustic  attachment;  in  other  respects  the  meters  are 
the  same. 

The  cable  should  be  of  iron  or  steel  of  sufficient  strength  to 
sustain  a  car  and  two  men,  and  should  be  securely  anchored  at 
both  ends.  The  car  should  be  about  5  ft.  x  3  ft.  x  1  ft.  deep, 
attached  at  each  end  to  a  pulley  on  the  cable.  If  the  stream  is 
deep  and  its  velocity  high  a  stay  line  will  be  required  to  hold 
the  meter  in  position.  This  line  should  be  located  about  100 
feet  upstream  from  the  cable.  The  following  dimensions  *  of 


*  Taken  from   "River   Discharge,"   by  Hoyt   and   Grover,  John  Wiley  & 
Sons,  New  York. 


EXAMINATION  AND  RECONNOISSANCE 


15 


cable  are  based  on  a  working  stress  of  about  16,000  pounds 
per  square  inch. 


Span  Feet 

Diameter  Inches 

Sag  Feet 

100 

l/2 

4 

.      200 

16 

6 

300 

8 

400 

M 

10 

500 
600 

V* 

12 
12 

700 

1 

14 

800 

11/8 

15 

The  methods  pursued  in  measuring  the  flow  with  current 
meters  in  rivers  and  canals  are  essentially  the  same,  and  will 
here  be  considered  together.  More  accurate  results  are  desired 
and  necessary  in  canal  measurements,  and  fortunately  the  con- 
ditions of  flow  and  cross-sections  of  channel  are  favorable  in 
most  cases  for  such  increased  accuracy.  Good  measurements  on 
canals  should  give  an  accuracy  within  2  or  3  per  cent,  while 
river  measurements  are  considered  good  if  they  give  within  5  to 
10  per  cent  of  the  true  discharge. 

Soundings,  either  with  a  meter  or  with  a  special  sounding 
line  and  weight,  should  be  made  at  the  permanent  measuring 
points.  The  mean  velocity  at  each  of  these  measuring  points 
should  then  be  determined  by  means  of  the  current  meter,  in 
accordance  with  one  of  the  approved  methods  of  determining 
mean  velocities.  There  are  five  general  methods  of  determining 
mean  velocities  in  a  vertical  line  with  a  current  meter:  (a)  by 
taking  the  velocity  at  0.2  and  that  at  0.8  of  the  water  depth 
and  obtaining  one-half  the  sum;  (b)  by  taking  the  velocity  at 
0.6  of  the  water  depth;  (c)  by  taking  the  velocities  at  equal 
vertical  intervals  of  0.5  of  a  foot  or  more,  and  obtaining  their 
arithmetical  mean,  or  finding  the  mean  value  from  a  curve 
derived  by  plotting  the  measurements  on  cross-section  paper; 
(d)  by  taking  the  velocity  near  the  water  surface  and  using 
from  0.85  to  0.95  of  the  result,  depending  on  the  depth  of  water, 
its  velocity,  and  the  nature  of  the  canal  bed;  and,  (e)  by  taking 
velocity  in  the  vertical  line  by  slowly  and  uniformly  lowering 
and  raising  the  meter  throughout  the  range  of  water  depth  one 


16  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

or  more  times.  Experiments  have  shown  that  the  0.2  and  0.8 
method  generally  gives  the  most  uniform  and  satisfactory  results. 
There  are  two  important  methods  of  computing  discharges 
from  measurements  made  by  current  meters.  Both  of  these 
methods  are  based  on  determining  the  discharges  of  the  elemen- 
tary areas  between  the  measuring  points  and  taking  their  sum. 
In  one  of  the  methods,  the  discharge  is  computed  separately  for 
each  elementary  area  on  the  assumption  that  both  the  velocity 
and  the  water  depth  vary  uniformly  from  one  measuring  point 
to  another.  This  may  be  termed  the  straight-line  method,  and 
the  formula  for  computing  the  discharge  of  the  elementary  area 
is  as  follows: 

(Va±Vj>\  (<*  +  l>\  i 

*  =  (— 2~ )  (-r)1' 

in  which  a  and  b  are  the  water  depths  in  feet  at  two  adjacent 
measuring  points,  Va  and  Vb  the  respective  mean  velocities  in 
feet  per  second  at  these  points,  /  the  distance  in  feet  between 
the  points,  and  q  the  discharge  in  second-feet  for  the  elementary 
area.  This  formula  is  well  suited  to  computing  discharges  in 
canals  conforming  in  cross-sections  to  their  original  trapezoidal 
or  rectangular  dimensions.  In  the  other  method,  the  discharge 
is  computed  for  consecutive  pairs  of  elementary  areas,  on  the 
assumption  that  the  velocities  and  the  water  depths  for  three 
consecutive  measuring  points  each  lie  on  the  arc  of  a  parabola. 
This  method  might  be  termed  the  parabolic  method  and  the 
formula  for  computing  the  discharge  for  each  pair  of  elementary 
areas  is  as  follows: 


.  .l 

q     \ e~  ~)  \     6     r 

in  which  a,  b,  and  c  are  the  water  depths  in  feet  at  three  consecu- 
tive measuring  points;  Va,  Vb,  and  Vc  the  respective  mean 
velocities  in  feet  per  second  at  these  points;  /  the  distance  in 
feet  between  the  consecutive  points,  and  q'  the  discharge  in 
second-feet  for  the  pair  of  elementary  areas.  This  formula  is 
more  particularly  applicable  to  river  channels  and  old  canals 
that  have  cross-sections  conforming  in  a  general  way  to  the  arc 
of  a  parabola,  or  to  a  series  of  arcs  of  different  parabolas. 


EXAMINATION  AND   RECONNOISSANCE  17 

The  discharge  measurements  at  a  current-meter  station  should 
be  taken  at  sufficient  intervals  of  gage  heights  to  permit  of 
making  accurate  velocity,  area,  and  discharge  curves.  For  this 
purpose  it  is  necessary  to  get  well-distributed  measurements  from 
low  to  high  stages.  Special  precautions  are  necessary  in  canal 
measurements.  The  canal  bed  at  a  well-selected  current-meter 
station  is  generally  permanent  in  character  and  a  permanent 
rating  curve  could  be  made  were  it  not  for  the  fact  that  increased 
•vegetable  growth  in  the  canal  and  on  its  banks,  during  the  irri- 
gation season,  together  with  accumulations  of  silt,  decrease  the 
discharge  capacity  for  all  gage  heights  during  the  latter  part  of 
the  irrigation  season.  This  fact  must  be  taken  into  consideration 
in  computing  the  quantity  of  water  carried  by  a  canal  during 
the  irrigation  season.  If  the  canal  is  cleaned  during  the  season, 
the  relation  of  discharge  to  gage  height  is  again  disturbed. 
These  changing  relations  of  discharge  to  gage  height  are  the  chief 
source  of  errors  and  difficulties  in  irrigation-canal  hydrography. 

In  order  to  determine  the  discharge  at  a  current-meter  sta- 
tion it  is  necessary  to  read  the  gage  daily  for  rivers,  and  for 
canals  additionally  at  such  times  as  changes  of  stage  are  made. 
The  gages  should  be  read  accurately,  generally  to  the  nearest 
hundredth  of  a  foot.  The  current-meter  measurements  at  a 
station  are  interpreted  and  extended  to  cover  all  gage  heights 
at  the  station  by  means  of  curves  drawn  on  cross-section  paper. 
To  construct  these  curves,  the  discharges  in  second-feet  as  com- 
puted from  individual  current-meter  discharge  measurements, 
the  corresponding  mean  velocities  in  feet  per  second,  and  the 
cross-sectional  areas  in  square  feet  for  each  measurement  are 
plotted  as  abscissas,  each  to  a  convenient  scale,  with  the  common 
gage  heights  as  ordinates.  The  most  probable  area  curve  is 
drawn  through  the  area  plottings  and  from  this  the  accuracy  of 
the  area  computations  and  of  the  soundings  are  checked  and,  in 
case  of  a  shifting  channel,  changes  in  the  rating  section  are  dis- 
covered. The  most  probable  velocity  curve  is  drawn  through 
the  velocity  plottings  on  the  sheet  to  provide  a  graphic  means 
of  finding  inaccuracies  in  the  computations  and  noting  dis- 
turbances in  the  velocity  due  to  obstructions  in  the  channel  or 
changes  in  the  velocity  due  to  increased  roughness  of  the  channel 


18 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


from  vegetable  growths  in  the  canal.  The  discharge  curve  is 
then  drawn  through  the  discharge  points  on  the  cross-section 
paper,  giving  due  weight  to  the  various  measurements  and  to 
products  .of  the  mean  velocity  and  area  abscissas  for  various 
gage  heights  throughout  the  range  of  depths.  Where  the  con- 
ditions of  flow  have  not  been  changed  during  the  season,  it  will 
generally  be  comparatively  easy  to  draw  a  satisfactory  curve. 
Where/ however,  the  relation  of  discharge  to  gage  height  has 
been  affected  by  vegetable  growth,  or  the  introduction  of  other 
obstructions,  these  conditions  must  be  given  careful  consideration 
and  another  curve  drawn  for  that  part  of  the  season  during  which 


4.0 
3.5 
|3.0 

I" 
|2.0 

i 

o1-5 

1.0 
0.5 

20        41 

Discharge  in  Second-f  e 
3        60        80       100       120      140      It 

Bt 
0       180       200       220 

*£_ 

z 

/ 

X 

X* 

Le/ 

'6 
i 

/ 

S 

^ 

<¥ 

/ 

t> 

* 

/ 

A 

'A 

k 

>< 

A 
^ 

a 

/ 

/ 

/ 

.*&, 

7 

/ 

/ 

,~<v^ 

/ 

./ 

AT 
5         1 

-a  in  S( 
)         1 

uarel 
)          2 

eet 
)         2 

5          3 

\ 

/ 

0 

^ 

^e,o 
2 

city  in 
3 

F/ctpi 

L    41 

rSeco 
5 

id 
6 

FIG.  2. — Example  of  Discharge,  Mean  Velocity,  and  Area  Curves. 

such  conditions  have  existed.  The  discharge  curve  for  these 
conditions  will  generally  be  parallel  to  the  discharge  curve  for 
the  earlier  part  of  the  season  when  the  channel  was  clean.  For 
the  period  during  which  the  change  is  in  progress,  the  discharges 
must  be  estimated  on  the  theory  of  proportion  from  the  two 
curves  constructed  for  the  extreme  conditions. 

By  means  of  daily  gage  heights  and  the  rating  tables,  the 
daily  discharges  may  readily  be  compiled,  and  the  summation  of 
these  gives  the  monthly  discharges  and  the  total  amount  of  water 
carried  during  any  period. 


EXAMINATION  AND  RECONNOISSANCE  19 

Prior  Water  Rights. — Before  the  quantity  of  water  available 
for  any  project  can  be  determined,  it  is  necessary  that  the  amount 
and  priorities  of  all  vested  water  rights  in  the  watershed  of  the 
proposed  project  be  definitely  determined  and  the  rights  of  all 
parties  fixed  in  order  that  the  available  supply  for  diversion  and 
storage  may  be  correctly  ascertained.  This  is  too  large  and 
complex  a  subject  to  be  discussed  here.  It  will  be  considered 
sufficient  to  say  that  it  may  have  a  large  influence  on  the  feasi- 
bility of  a  project.  It  is  well  to  obtain  legal  advice  in  these 
matters. 

Reservoirs  Available. — If  the  examinations  previously  dis- 
cussed show  that  the  monthly  flow  of  the  stream  at  the  proposed 
point  of  diversion  after  deducting  priorities  is  not  sufficient  for 
the  needs  of  the  project,  means  will  have  to  be  provided  for 
increasing  this  flow  during  the  irrigation  season,  either  by 
storage  of  the  winter  flow  of  the  stream  in  question  or  by  diver- 
sion of  water  from  an  adjacent  watershed.  To  this  end,  a  care- 
ful reconnoissance  of  the  headwaters  of  the  stream  is  necessary, 
which  should  supply  approximate  data  as  to  possible  dam  sites, 
together  with  the  nature  of  foundations  at  these  sites;  the  geo- 
logic formation  of  the  reservoir  bed  and  capacity  of  reservoir; 
the  probable  flow  of  the  stream  at  the  dam  site;  materials  avail- 
able for  construction,  and  all  other  information  that  might  have 
a  bearing  on  the  feasibility  of  the  sites  that  does  not  require  too 
much  time  and  expense  to  ascertain.  If  no  dam  or  reservoir 
sites  are  found  on  the  stream  itself,  examination  should  be  made 
of  the  surrounding  country  to  determine  if  there  are  any  feasible 
sites  to  which  a  feed  canal  could  be  constructed  from  the  main 
stream  or  its  tributaries.  Examination  should  be  made  of  adja- 
cent watersheds  and  streams,  and  the  dividing  ridges,  to  ascertain 
if  it  would  be  feasible  to  divert  water  from  one  watershed  to  the 
other  and  the  probable  quantity  of  water  that  could  be  so 
diverted. 

These  examinations  must  necessarily  be  of  a  rough  nature, 
as  detailed  examinations  are  usually  expensive.  The  topographic 
sheets  of  the  U.  S.  Geological  Survey,  if  available,  are  of  great 
assistance  for  this  purpose,  as  are  also  the  surveys  made  by  the 
engineering  departments  of  the  several  States. 


CHAPTER  II 
INVESTIGATIONS  AND  SURVEYS 

Water  Duty;  Quantity  Applied  to  Land. — An  examination  of 
an  irrigation  project  necessarily  involves  a  determination  of  the 
quantity  of  water  required  to  mature  crops.  In  most  arid 
regions,  irrigation  has  been  practised  in  one  form  or  another, 
and  the  quantity  of  water  actually  used  in  such  cases,  of 
which  there  is  generally  some  record,  provides  perhaps  the 
best  criterion  for  a  determination  of  the  quantity  of  water 
required. 

Reliable  information  on  the  quantity  of  water  actually  applied 
to  the  land  and  used  for  maturing  crops  is  very  meagre.  This  is 
largely  due  to  the  fact  that  very  few  projects  have  been  equipped 
with  accurate  measuring  devices  and  in  many  cases  the  water 
diverted  to  the  land  even  when  measured  has  been  largely  in 
excess  of  the  requirements,  and  no  record  was  kept  of  the  quan- 
tity wasted.  Fortunately,  due  to  the  Government's  interest  in 
irrigation  matters,  and  because  of  the  increasing  scarcity  of  un- 
appropriated water,  accurate  records  are  now  being  kept  on 
many  projects,  and  in  the  course  of  the  next  few  years  good 
data  will  probably  be  available. 

The  quantity  of  water  required  for  irrigation  depends  on 
the  amount  of  rainfall,  length  of  irrigation  season,  nature  of 
soil,  kind  of  crop,  and,  to  a  very  large  extent,  upon  the  efficiency 
with  which  the  water  is  handled.  Sandy  and  gravelly  soils  re- 
quire more  water  than  volcanic  ash  and  clayey  soils.  Hay  and 
vegetables  require  more  water  than  fruits  and  grains.  Continu- 
ous irrigation  with  a  small  head  of  water  results  in  a  loss  that  is 
avoided  when  intermittent  applications  are  made  with  larger 
heads.  The  quantity  of  water  applied  to  the  land  on  some  of 
the  Government  reclamation  projects  is  contained  in  the  fol- 
lowing tabulation: 

20 


INVESTIGATIONS  AND   SURVEYS 


21 


oi     . 

•g  c 


• 

.      6 

Ii 


C 

«» 


-_c 

Eg      x 

II  ! 


1 


L  II  l  H 

-rl  .84  .^     .«^ 


uoseag 


_          .    fl 
COts~iOCO^frlC<liO'-HGO' 

CO  CO  CO  <N  <N  T-J  T-l  T-H  TH  TH    <N  <N  T-l  T-H  rH  rH  TH  <N  T-H  <N 

OiOOrJH'*  (NOOOO       O  iO  CO  O  O  <N  O  cp  CO  O 

CO  <N  ci  CO  C<i  C<i  <N  lO  lO  TjH        id  O5  CO  CO  CO  GO  CO  CO  >O  !>;  > 

>-"-!  00  O -^  GO  Oi  O  <M  (M        »O  Ol  CO  I><N  t>«  O  »-t  <N  GO 
TfiOCOC^iOT— ii-HC^C^^f        C^iOT— I^HT— ii-HCQCOC^lCO 

»OcOGOOcOiOI>O<MtO       O5     •  TH  TH  <N  (N  CO  »-i  b-  O  ^ 

I 

00  CO  !>•  GO  CO  O5  1>  O  t>  »O   CO  O5  C<l  CO  "*  O5  O5  GO  <N  Oi     « 

I  *4  ,4  g>  *4  C4  C4  00    ^ 

CO  CO  O^  t^»  CO  ^^  CO  ^5  O^  1s*       ^^  O^  O^  0^  ^*  ^^  O^  GO  T^  ^^          •— • 
CO  TJH  <N  rH  N!  <M'  (N  oi  CO  TjH       (N  id  O  i-i  i-i  (N  I-H  (N  <N  CO 

1  C1     •     •  i^  O^        CO     *  ^^  4s*  t^*  1^*     •  ^O  ^O     •  jy 

•IOCOC5      .(M     •      •  CO  rJH        <N      -r-iT-idci      -CO(M 

•     •     •     •     •  iO     •     •  <N     •       CO     •  O  <N     •     •     •  iO  CO 

'coci    •        % 

:Q  :  : 


m 


9«5-|  :-S 


22 


WORKING  DATA   FOR   IRRIGATION   ENGINEERS 


CM  ^  00  CO 


CO  CO  t"*»  CO  O^  *O  ^O  CO 
'—  'GOOlcMi—  iQOl^O 


CM  ooi>-  1—  i  o  CM  co  oo  Ci  i—  •  Ci»oooocoQi'^n>i>»o 

iO*OO500l>COCOOiTtir>.rHCMiOOOi—  iCOtMOCMcO 
CO  •*  CO  •<*  rH  CM'  T}<  rH  rH  r4  r-^  (N  Oi  (N  T-H  FH  ^-1  CO  (N  TH 


:  :  :g 


t-  TJH  O  O5  '-i  1C  CO      •      •      -CM      -iQO      •      •      -CO      "-i 
^COCOCOOO^H      .      .      -0      -O^H      •      •      -(N      -0 


rH  OS  CM  IO  rH  00  CO  CM  rH  rH  O  Oi  00  IO  rH       •  Tt  CO  O 
^lOCMt^rHCM'OqrHqqTjHCMrHqrH        •  CO  IN  rH 

-eg — u_: 


3  •«*  CO  O5  CM  CO 


OCMO'—  " 


<«O500      -CMOCM O5  lO     .     .     -CO     -Q 

13 co CM    •  q q  —j co ^    •    •    -CM    •  q 


CO  rH  CO  !>•  -^  O        CN  i—  I        I-H  CO  CO  CM  CO        O5CO 

i-H  CO  T-H  i-H 


CO  t>*  CO  Is*  ^^  00  O5 


1 


1 


was  measured  at  the 

system  estimated  at 
figure  is  used  in  esti- 


October  22. 
ed  to  the  lan 

ses  in  latera 
weirs,  and  th 


was  turned  in  April  12  and  turned  o 
Idaho-Minidoka.  —  The  water  deli 
heads  of  laterals. 
Wash.-Yakima-Sunnyside  Unit.— 
15%  of  amounts  measured  at  the  he 
mating  amount  delivered  to  farms. 


re  Valley.—  The  apparently  high  percentage  of  water 
delivered  to  the  land  was  due  to  the  fact  that  water  was 
canals  through  additional  feeder  canals  not  measured. 
ctly  under  the  U.  S.  R.  S. 
e  upper  system  receives  water  directly  from  the  main 
ystem  receives  water  from  the  Deer  Flat  Reservoir.  In 
ater  was  turned  in  February  5,  in  the  latter  system  water 


Colo.-Uncompa 
diverted  which  wa 
also  supplied  to  the  c 
Area  is  for  that  direct 
Idaho-Boise.—  The 
canal.  The  lower 
the  former  system 


INVESTIGATIONS  AND   SURVEYS  23 

This  table  is  intended  to  give  a  general  idea  of  what  may 
be  expected  under  similar  conditions  elsewhere.  The  average 
applications  may  be  considered  as  rather  high  for  permanent 
conditions  for  the  reason  that  many  of  these  lands  are  new  and 
require  considerably  more  water  than  will  be  necessary  ulti- 
mately. In  general,  it  may  be  stated  that  more  water 
was  applied  to  the  land  than  was  absolutely  necessary  for 
growing  the  crops,  so  that  in  time,  when  the  irrigators 
become  more  proficient  and  water  becomes  more  scarce,  the 
quantity  applied  to  the  land  will  no  doubt  be  considerably 
reduced. 

Distribution  of  Irrigation  Water  through  the  Season. — It  is 
not  sufficient  to  know  the  total  quantity  of  water  that  is  required 
in  a  season,  but  it  must  also  be  known  how  the  use  of  this  water 
is  to  be  distributed  through  the  season.  This  is  necessary  for 
determining  the  sufficiency  of  the  water  supply  during  the  irriga- 
tion months,  when  storage  is  not  provided,  and  also  to  determine 
the  maximum  capacity  of  canals.  It  is  obvious  that  more  water 
is  required  during  the  hot,  dry  summer  months  than  earlier  and 
later  in  the  season.  Fortunately,  a  general  knowledge  of  the 
variation  in  the  requirements  for  the  different  months  is  sufficient, 
as,  if  necessary,  the  quantities  used  can  be  adjusted  in  a  consid- 
erable degree  to  the  available  supply.  Generally  speaking,  the 
maximum  requirement  may  be  taken  as  25  to  50  per  cent  greater 
than  the  average.  The  accompanying  table  is  useful  as  furnish- 
ing general  data  on  the  distribution  of  water  throughout  the 
season.  This  table  also  gives  the  relation  of  the  quantity  deliv- 
ered to  the  land  to  the  quantity  diverted  into  the  main  canal  of 
the  system.  The  difference  does  not  represent  the  amount  lost  by 
seepage,  as  in  most  cases  a  considerable  portion  of  the  quantity 
diverted  was  wasted  through  wasteways  and  returned  directly 
to  the  river.  To  obtain  quantity  lost  by  seepage,  the  quantities 
wasted  must  first  be  deducted  from  the  diversion,  and  the  re- 
mainder is  then  the  sum  of  the  quantities  applied  to  the  land,  and 
the  quantities  lost  by  seepage.  These  sums,  less  the  applied  quan- 
tities given  in  the  table,  give  the  seepage  losses  in  the  entire 
system.  These  are  shown  in  the  following  tabulation  as  far  as 
the  figures  are  available: 


24  WORKING  DATA  FOR  IRRIGATION   ENGINEERS 

TABLE    11 


Project 

Total  Canal  Losses  in 
Percent  of  Diversion, 
1912 

Project 

Total  Canal  Losses  in 
Percent  of  Diversion, 
1912 

Yuma 

32 

Carlsbad 

48 

Orland  

20 

Klamath 

36 

Boise  

37 

Belle  Fourche 

32 

Minidoka  

27 

Okanogan 

47 

Flathead  

50 

Sunnyside. 

27 

Huntley 

17 

Tieton 

17 

Sun  River 

26 

Shoshone 

36 

Lower  Yel'stone. 
North  Platte  .    . 

43 
21 

Average 

32% 

Truckee-Carson  . 

34 

NOTE. — See  Table  14,  page  44,  for  seepage  losses  from  canals  in  various 
materials. 

It  has  often  been  assumed  in  investigations  of  irrigation 
projects,  that  one-third  of  the  quantity  diverted  would  be  lost 
by  seepage  and  evaporation  in  the  canal  system,  and  the  above 
average  seems  to  support  this  assumption.  A  detailed  consider- 
ation of  seepage  losses  for  the  purpose  of  designing  canals  is 
taken  up  later.  A  loss  by  seepage  in  the  entire  system  of  one- 
third  the  quantity  diverted  is  considered  to  be  sufficiently  ac- 
curate for  preliminary  purposes. 

Location  of  Point  of  Diversion. — The  first  examination  will 
have  indicated  in  a  general  way  the  elevation  at  which  it  is 
necessary  to  divert  in  order  to  cover  a  suitable  body  of  land,  and 
with  this  knowledge  the  stream  must  be  examined  for  a  suitable 
location  for  diversion  works  which  will  give  the  necessary  eleva- 
tion. In  most  cases  it  will  be  necessary  to  dam  the  stream,  and 
it  is  then  necessary  to  estimate  the  area  of  flooded  lands  in  order 
to  determine  the  amount  of  damages  that  will  have  to  be  paid 
to  the  owners  for  such  flooding.  For  the  present  purposes,  only 
a  rough  approximation  of  the  flooded  area  is  necessary,  but  ulti- 
mately careful  calculations  for  determining  the  elevations  of  the 
backwater  must  be  made.  The  bed  and  banks  of  the  river  should 
be  examined  for  suitable  foundations  for  dam  and  headworks,  so 
that  the  general  type  of  dam  required  can  be  determined.  Cross- 
sections  of  the  stream  must  be  measured,  and  some  topography 
(which  can  be  taken  at  small  expense)  is  helpful.  The  general 
type  of  dam  and  its  length  and  height  should  be  determined  upon 
and  an  estimate  of  quantities  prepared. 


INVESTIGATIONS  AND   SURVEYS  25 

Location  of  Main  Canal. — Having  determined  upon  the  loca- 
tion of  a  point  of  diversion,  the  location  of  the  main  canal  may 
be  started.  (Not  infrequently  it  happens  that  the  point  of 
diversion  is  dependent  upon  the  location  of  the  main  canal, 
especially  in  rough  country.)  From  the  considerations  already 
discussed,  the  size  and  grades  of  the  canal,  upon  which  depends 
its  location,  may  be  determined.  The  size  and  grades  of  the 
canal  should,  of  course,  be  adjusted  to  the  requirements  of  the 
land  to  be  supplied,  but  a  rough  determination  will  suffice  for 
preliminary  purposes,  and  after  the  location  has  been  surveyed 
and  platted  and  a  better  knowledge  is  had  of  the  areas  to  be  irri- 
gated the  canal  sections  can  readily  be  increased  or  reduced 
within  certain  limits  without  causing  appreciable  errors  in  the 
estimates. 

Assuming  that  the  irrigable  lands  are  located  in  an  elongated 
valley  bordered  by  higher  lands  more  distant  from  the  stream, 
the  main  canal  will  follow  along  the  highest  points  of  the  irrigable 
area,  generally  skirting  along  the  foothills,  following  around  the 
wider  valleys  of  tributary  watercourses,  and  jumping  across  the 
narrower  ones.  A  preliminary  location  for  the  purpose  of  esti- 
mates requires  the  use  of  a  transit  and  level,  but  great  refinement 
is  not  necessary.  Long  shots  may  be  taken  with  the  level  and 
the  stadia  may  be  used  for  measuring  distances,  only  angle  points 
being  set  and  no  curves  run.  In  very  rough  locations  it  is  neces- 
sary to  set  a  large  number  of  angle  points  if  fair  estimates  are 
desired.  After  the  fly-line,  or  a  portion  of  it,  has  been  run,  the 
level  party  should  go  over  the  line  and  take  elevations  and  trans- 
verse slopes  at  sufficiently  frequent  intervals  to  enable  a  profile 
to  be  drawn  from  which  to  estimate  earthwork  quantities,  and 
structures  such  as  flumes,  pipes,  etc. 

Determination  of  Irrigable  Area. — The  main  canal  will  gen- 
erally be  the  upper  boundary  of  the  irrigable  area,  and  the  stream 
the  lower  boundary  from  which,  after  platting,  the  included  area 
is  measured.  There  must  also  be  made  surveys  of  the  lands 
which  are  non-irrigable,  or,  in  other  words,  not  tillable,  such  as 
rocky  land,  swamp  land,  etc.,  and  areas  which  are  isolated, 
that  is,  too  high  to  reach  by  gravity  from  the  main  canal.  The 
boundaries  of  non-irrigable  and  isolated  lands  may  be  run  by 


26  WORKING  DATA   FOR   IRRIGATION   ENGINEERS 

transit  and  stadia.  If  the  country  has  been  subdivided  into 
townships  and  sections,  all  surveys  should  be  tied  to  land  lines; 
otherwise  it  will  be  necessary  to  make  surveys  to  tie  all  the 
above-mentioned  surveys  together.  The  areas  of  non-irrigable 
and  isolated  lands  are  measured  and  deducted  from  the  total  to 
get  the  net  area  irrigable,  after  which  it  may  be  advisable  to 
modify  the  capacities  and  sizes  of  canal  sections  on  which  the 
canal  location  was  based.  These  revisions  may  affect  the  esti- 
mates of  quantities,  but  a  relocation  of  the  line  for  estimating 
purposes  will  not  generally  be  required. 

Reservoir  Surveys. — These  should  be  of  sufficient  accuracy 
to  give  the  probable  capacity  of  the  reservoir  within  10  to  20 
per  cent.  If  the  reservoir  is  a  natural  lake,  the  survey  should 
include  an  investigation  of  the  possibility  of  storage  by  lowering 
the  lake  outlet  by  tunnel  or  trench  excavation;  the  boundary  of 
the  lake  should  be  meandered  and  profiles  run  up  the  slopes  at 
frequent  intervals  to  an  elevation  high  enough  to  cover  the 
highest  elevation  to  which  the  water  may  be  raised.  The  volume 
may  then  be  found  by  measuring  the  areas  at  successive  5-  or 
10-foot  contour  intervals,  and  computing  the  volume  between 
by  the  usual  methods;  if  it  is  possible  to  lower  the  surface  of  the 
lake  these  profiles  should  be  carried  below  the  water  surface  by 
soundings.  If  the  reservoir  site  is  dry,  a  base  line  should  be 
established,  and  the  topography  elaborated  from  the  same 
by  the  use  of  the  transit  and  stadia  or  plane  table.  From  the 
topographic  sheet  the  capacity  is  calculated  as  noted  above.  A 
topographic  survey  of  the  dam  site  should  be  made,  together 
with  sufficient  test  pits  or  borings  to  give  a  general  indication  of 
the  nature  of  the  foundations. 

A  scale  of  400  feet  to  one  inch,  with  10-foot  contour  intervals, 
will  ordinarily  be  found  satisfactory  for  the  reservoir  site.  For 
the  dam  site,  a  scale  of  40  feet  to  one  inch  and  contour  intervals 
not  greater  than  five  feet  should  ordinarily  be  used.  The  best 
scales  and  contour  intervals  depend  upon  the  local  conditions, 
but  those  mentioned  have  given  satisfactory  results  in  many 
surveys  for  quite  a  wide  range  of  conditions. 

General  Remarks  on  Canal  Locations. — In  making  locations 
of  canals  the  question  of  cost  as  affected  by  location  is  of  prime 


INVESTIGATIONS   AND   SURVEYS  27 

importance.  In  most  systems  the  canal  excavation  consti- 
tutes by  far  the  greater  part  of  the  construction  cost  of  the  proj- 
ect, and  canal  maintenance  constitutes  a  very  large  portion  of 
the  maintenance  costs.  The  first  cost  is  often  relatively  less  im- 
portant than  cost  of  operation  and  maintenance,  and  the  locating 
engineer  must  keep  both  in  mind.  It  is  a  comparatively  simple 
matter  to  locate  a  canal  so  as  to  obtain  the  least  quantity  of 
earthwork,  and  this  is  susceptible  of  exact  mathematical  estab- 
lishment, but  maintenance  and  operating  cost  are  not  so  easily 
calculated.  No  set  rules  can  be  formulated  for  proper  locations 
to  give  minimum  operation  and  maintenance  costs.  This  must 
be  left  almost  entirely  to  the  experience  and  judgment  of  the 
locating  engineer.  The  value  of  experience  in  this  matter  can- 
not be  overestimated,  and  a  knowledge  of  operation  and 
maintenance  of  canals  is  necessary  to  obtain  an  economic 
location. 

In  locating  a  canal,  effort  should  be  made  to  keep  the  water 
section  in  cut  as  far  as  practicable,  and  high  fills  should  be  avoided 
as  much  as  possible  on  large  canals,  as  they  are  a  source  of  endless 
danger  and  expense  in  operation  and  maintenance.  One  of  the 
most  important  items  to  be  kept  in  mind  is  that  the  water  surface 
must  be  kept  high  enough  to  reach  the  adjacent  land  after  an 
allowance  has  been  made  of  sufficient  drop  to  make  a  measure- 
ment of  the  water  over  a  weir  or  other  measuring  device.  This 
is  especially  true  of  the  smaller  distributaries  from  which  the 
water  is  taken  directly  onto  the  land,  and  if  neglected  when  the 
canal  is  constructed,  the  possibility  of  properly  measuring  the 
water  may  be  irreparably  lost,  or  the  expense  of  rectifying  the 
damage  be  very  high,  whereas  the  expense  of  making  provision 
for  a  measurement  when  the  canal  was  built  would  have  added 
little  to  the  cost.  The  proper  drop  in  water  surface  to  allow  for 
making  a  measurement  depends  upon  the  quality  of  water  to  be 
measured,  and  the  kind  of  device  to  be  used  for  measuring,  both 
of  which  should  be  definitely  known  before  the  location  is  made. 
It  must  also  be  remembered  that  it  may  be  necessary  to  make 
these  measurements  when  the  canal  is  not  operating  at  its  max- 
imum capacity,  and  unless  means  are  provided  for  checking  up 
the  water  to  maximum  elevation  the  measurement  must  be  made 


28  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

at  a  lower  elevation.  An  adjustment  must  be  made  between  the 
cost  of  raising  the  grade  of  the  canal,  providing  checks  for  back- 
ing up  the  water,  or  cutting  out  a  certain  amount  of  land  adjacent 
to  the  canal  to  provide  the  necessary  drop  when  the  canal  is  not 
running  full. 


CHAPTER  III 

DESIGN  OF   IRRIGATION   STRUCTURES 

To  design  irrigation  structures  properly  requires  a  thorough 
knowledge  of  structural  and  hydraulic  engineering.  In  addition 
to  this,  a  knowledge  of  the  special  requirements  of  irrigation 
structures  is  necessary.  Mechanical  details  of  design  are  not 
here  discussed,  but  the  broad  problems  connected  therewith  are 
pointed  out,  and  aids  for  their  solution,  in  the  form  of  tables 
and  diagrams,  are  presented. 

Storage  Works. — The  rapidly  decreasing  supply  of  unappro- 
priated water  from  the  natural  flow  of  streams  has  in  the  past 
few  years  made  the  problem  of  storage  works  increasingly  im- 
portant. The  problem  is  a  very  difficult  one — perhaps  the  most 
difficult  of  all  that  the  irrigation  engineer  encounters — and  only 
brief  mention  can  be  made  here  of  some  of  its  principal  features. 

Naturally,  the  first  point  to  be  decided  is  the  water  supply 
available  for  storage.  This  has  already  been  discussed,  but  an 
additional  factor  not  previously  considered  is  the  probable 
evaporation  from  the  reservoir.  This  is  especially  important  in 
shallow  reservoirs.  The  velocity  of  the  wind  and  the  total  wind 
movement  have  a  considerable  influence  on  the  evaporation. 
The  evaporation  is  greater  in  humid  than  in  arid  regions  and 
increases  with  the  temperature.  For  these  reasons  a  much  greater 
allowance  must  be  made  for  the  evaporation  from  a  reservoir 
located  in  a  valley  on  the  plains  than  from  a  reservoir  in  the 
mountains  where  the  temperatures  are  lower,  the  atmosphere 
more  humid,  and  the  water  surface  more  or  less  protected  from 
the  sweep  of  the  winds.  Experiments  made  in  1909-10  by  the 
Weather  Bureau,  United  States  Department  of  Agriculture,  gave 
the  figures  in  Table  12  for  the  monthly  and  annual  evaporation  at 
various  places,  mostly  in  the  Western  States.  The  measurements 
were  made  in  pans  on  the  ground,  floating  in  water,  or  elevated 
on  stands.  Calculations  made  by  the  experimenters  indicate 
that  the  evaporation  from  a  pan  2  feet  in  diameter  is  about  75 
per  cent,  that  from  a  pan  4  feet  in  diameter  is  about  50  per  cent, 

29 


30 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


and  that  from  a  pan  6  feet  in  diameter  is  about  30  per  cent 
greater  than  the  evaporation  from  a  large  pond  or  lake.  The 
figures  in  the  table  may  be  roughly  corrected  on  this  basis;  thus, 

TABLE   12 

TOTAL  AMOUNT  OF  EVAPORATION  BY  MONTHS 

The  figures  contained  in  these  tables  have  not  been  corrected  for  the 
wind  effect,  the  temperature  effect,  the  vapor-pressure  effect,  nor  for  the 
size  of  the  pans,  but  they  represent  the  observed  evaporation  at  the  pan  as 
located.  D  is  the  diameter  of  pan  in  feet. 


Number  

l 

2 

3 

4 

5 

Station  

Salton  Sea, 
1,500  Ft. 

Salton  Sea, 
500  Ft.  at 

Salton  Sea, 
7,500  Ft.  at 

Indio,  Cal. 

Mecca,  Cal. 

Inland 

Sea 

Sea 

Position  of  Pans 

Ground  D  =2 

D  =4 

D  =4 

Ground  D=6 

Ground  D=6 

January 

5.08 

3.61 

3.41 

3.18 

2  92 

February  

7.42 

5.01 

5.09 

5.08 

5  00 

March  
April  

12.50 
15.75 

6.75 
9.00 

6.95 

8.75 

7.50 
12.05 

8.07 
10.87 

Mav.  • 

19.00 

11.00 

10.50 

15.84 

12.72 

i  Lay 

June  

21.50 

13.50 

13.00 

16.11 

14.23 

July 

22  15 

14.77 

14  03 

16  34 

15  21 

J*"j  
August 

18  50 

12.53 

12  19 

13  78 

13  22 

September  
October  
November 

15.50 
13.19 

7.49 

12.40 
9.20 
6.21 

12.08 
9.24 
5.96 

12.37 
8.91 
5.17 

10.29 

8.17 
4  13 

December  .  .      .    . 

6.42 

4.67 

5.25 

3  00 

2.98 

Year  

164.50 

108.65 

106.45 

119.33 

107.81 

Number  

6 

7 

8 

9 

Station  

Brawley, 
Cal. 

Mammoth, 
Cal. 

N.  Yakima, 
Wash. 

Hermiston, 
Oreg. 

Position  of  Pans 

Ground  D=6 

Ground  D=6 

Ground  D  =4 

Raft  D  =4 

Ground  D=a 

January 

3.05 

5.00 
8.00 
10.74 
13.79 
13.68 
14.14 
11.26 
10.15 
6.99 
4.09 
2.66 

4.24 

5.67 
8.99 
12.02 
15.52 
16.75 
18.00 
13.73 
12.16 
9.49 
5.26 
3.70 

1.75 
2.50 
6.25 
7.91 
8.36 
8.90 
10.74 
9.41 
5.51 
3.15 
2.00 
1.50 

1.25 
1.25 
3.00 
7.28 
7.89 
9.54 
12.04 
11.07 
7.35 
3.88 
2.00 
1.50 

1.50 
1.75 
4.25 
9.28 
11.38 
13.84 
17.48 
16.89 
10.09 
6.08 
3.00 
1.75 

February  
March  
April  . 

Mav.  • 

i  Lay 

June  

July  
August  
September  
October  
November. 

December  
Year  

103.55 

125.53 

67.96 

68.05 

97.29 

DESIGN  OF   IRRIGATION  STRUCTURES 

TABLE   12  (Continued) 
TOTAL  AMOUNT  OF  EVAPORATION  BY  MONTHS 


31 


Number  

10 

11 

12 

Station  

Granite  Reef,  Ariz. 
Salt  River 

California,  O. 
Filtration 
Plant 

Birmingham,  Ala. 
East  Lake  Reservoir 

Position  of  Pans 

Ground 
D  =4 

Floating 
D  =  4 

Floating 
D  =  4 

Floating 
D  =4 

Floating 
D  =4 

Ta.nua.ry 

4.59 
4.75 
6.25 
9.00 
11.50 
13  50 
14.25 
14.23 
13.76 
11.31 
7.39 
4.65 

4.25 
4.40 
5.25 
7.00 
9.50 
12.00 
12.75 
12.50 
11.00 
8.31 
6.56 
4.22 

1.00 
1.50 

2.50 
4.12 
5.07 
6.21 
7.20 
7.26 
5.63 
3.00 
1.50 
1.00 

1.50 

1.50 
2.25 
4.45 
5.91 
7.28 
7.36 
7.34 
6.00 
4.00 
2.25 
1.50 

1.50 
1.50 
2.25 
5.36 
6.36 
7.54 
6.96 
7.32 
5.59 
4.00 
2.25 
1.50 

February 

March 

April  
May  
Tune 

Tulv 

August  
September 

October 

November  
December  

Year 

115.18 

97.74 

45.99 

51.34 

52.13 

Number  

13 

14 

15 

16 

17 

Station  

Dutch 
Flats, 
Nebr. 
Interstate 
Canal 

Minidoka 
Dam, 
Idaho. 
Snake 
River 
10  Feet 
Above 
Surface 

Deer  Flat,  Idaho 
Boise  Project 

Lake 
Kachess, 
Wash., 
10  Feet 
Above 
Surface 

Ady,  Kla- 
math, 
Oreg. 

Position  of  Pans 

Ground 
D  =4 

D  =3 

Ground 
D  =3 

Raft 
D  =  4 

D  =3 

Floating 
D  =4 

January 

1.75 
1.75 
3.00 
4.50 
6.25 
8.05 
10.95 
9.39 
7.44 
5.59 
4.00 
3.00 

2.25 
2.50 
4.00 
7.00 
11.21 
12.31 
15.00 
13.50 
11.00 
8.50 
5.75 
3.50 

1.50 

2.25 
4.00 
7.25 
10.68 
11.05 
11.15 
11.77 
9.75 
5.40 
2.70 
1.50 

2.00 

2.75 
4.25 
6.00 
7.90 
9.59 
10.59 
12.16 
9.25 
5.42 
5.52 
2.00 

0.50 
0.50 
1.25 
2.57 
3.83 
5.54 
5.93 
5.51 
4.41 
1.47 
0.75 
0.50 

0.50 
1.25 

3.57 
6.64 
7.15 
6.99 
8.01 
9.21 
6.13 
2.50 
1.00 
0.50 

February 

March 

April 

May  
June  
Tuly 

August  
September  
October  
November  
December  

Year  

65.67 

96.52 

79.00 

77.43 

32.76 

53.45 

32  WORKING  DATA   FOR  IRRIGATION   ENGINEERS 

TABLE   12  (Concluded) 
TOTAL  AMOUNT  OF  EVAPORATION  BY  MONTHS 


Number  

18 

19 

20 

21 

22 

23 

Station  

Fallen, 

Lake 
Tahoe, 

Elephant 
Butte, 

Carlsbad. 
N.  Mex. 

Alfalfa 
Field  near 

Lake 
Avalon, 

Nev. 

Cal. 

N.  Mex. 

At  Reclama- 
tion Office 

'  Carlsbad 

Pecos  River 

Position  of  Pans 

Floating 
D  =4 

2  Feet 
D  =4 

Ground 
D  =4 

Ground 
D  =4 

Ground 
D  =4 

Floating 
D  =4 

January  
February  

1.75 
1.75 

1.75 

1.75 

2.50 
2.75 

5.00 

5.50 

5.00 

5.25 

4.50 
4.50 

March  

2.25 

1.75 

4.50 

8.94 

8.95 

5.51 

April  

3.25 

2.00 

8.00 

11.68 

11.09 

7.45 

May  

5.25 

3.00 

11.50 

12.86 

10.95 

10.12 

June 

7  86 

4  25 

13  45 

12  40 

9  06 

11.05 

July 

9  86 

6.19 

11.57 

12  00 

10.58 

12.88 

J»    *   ' 
August    

8.70 

7.08 

10.48 

11.03 

9.32 

12.00 

September  
October  

5.13 
3.35 

6.22 
3.60 

8.58 
6.76 

9.76 

7.58 

7.84 
5.88 

9.50 
7.00 

November  
December 

2.50 
2  00 

2.62 
2  00 

3.86 
3  00 

5.50 
5.00 

5.43 
5.00 

5.75 
4.50 

Year  

53.65 

42.21 

86.95 

107.25 

94.35 

94.76 

The  true  evaporation  from  a  large  pond  or  lake  at  Dutch  Flats, 
Nebraska  (No.  13),  would  be  65.67  -=-  1.50  =  43.8.  The  evapor- 
ation from  a  pan  elevated  10  feet  above  the  ground  surface  aver- 
ages about  15  per  cent  greater  than  from  the  same  size  pan  on 
the  ground;  thus,  the  true  evaporation  from  a  3-foot  pan  at  the 
ground  surface  at  Lake  Kachess,  Wash.  (No.  16),  is  32.76  ^  1.15 
=  28.5  inches. 

The  seepage  from  the  floor  and  sides  of  a  reservoir  may  have 
a  large  influence  on  its  storage  capacity.  The  seepage  is  depend- 
ent upon  the  nature  of  the  material  composing  its  bottom  and 
sides,  and  the  location  of  the  ground-water  plane  in  the  vicinity. 
The  latter,  together  with  the  elevation  of  the  water  in  the  reser- 
voir, will  establish  the  grades  on  which  the  seepage  water  will 
flow  from  the  reservoir.  It  follows,  then,  that  these  grades  will 
produce  a  certain  velocity  of  water  through  the  material  in  the 
surrounding  country,  and  consequently  the  porosity  of  this 
material  may  have  a  greater  effect  on  the  volume  of  seepage 
than  the  porosity  of  the  material  composing  the  bottom  and 
sides  of  the  reservoir. 


DESIGN   OF   IRRIGATION   STRUCTURES  33 

Various  types  of  storage  dams  are  used,  the  most  important 
being  masonry,  earth,  rock-fill,  and  various  combinations  of 
these  three.  The  best  type  for  a  particular  location  depends 
upon  the  nature  of  the  foundations,  profile  of  dam  site,  material 
available  for  dam  construction,  accessibility  of  site,  etc.  A  site 
having  good  rock  foundations  and  abutments  is  usually  favorable 
for  a  masonry  dam.  If  the  canon  walls  are  steep  and  the  canon 
comparatively  narrow,  an  arched  masonry  dam  may  be  the 
best.  Excavations  have  been  dug  from  50  to  100  feet  deep  to 
obtain  suitable  foundations  for  high  masonry  dams.  Where  a 
continuous  solid  rock  foundation  cannot  be  had,  or  where  the 
cost  of  materials  for  a  masonry  dam  would  be  prohibitive,  a  rock- 
fill  or  earth  dam,  or  combination  of  the  two,  is  adaptable. 

Every  storage  dam  across  a  stream  having  an  unregulated 
flow  must  be  provided  with  a  spillway  which  should  preferably 
discharge  the  water  some  distance  downstream  from  the  toe  of 
the  dam  so  as  not  to  endanger  the  foundations  of  the  dam  and, 
in  the  case  of  earth  dams,  cause  erosion  by  backwash.  The 
records  of  flow  of  a  stream  do  not  usually  include  the  maximum 
probable  discharge,  which  is  exceedingly  difficult  to  predict. 
The  maximum  discharge  that  might  occur  must  be  assumed 
several  times  the  maximum  recorded,  depending  upon  the  length 
of  time  covered  by  the  records.  Fortunately,  a  reservoir  will 
generally  act  as  a  regulator  of  the  flow,  and  it  will  not  usually 
be  necessary  for  the  spillway  to  discharge  the  water  at  the  same 
rate  that  it  comes  into  the  reservoir.  Table  13  gives  the 
maximum  rate  of  discharge  of  streams  in  the  United  States 
as  determined  by  the  Hydrographic  Branch  of  the  United 
States  Geological  Survey.  A  study  of  this  table  will  give 
some  idea  of  the  probable  maximum  discharge  from  a  given 
stream. 

The  location  and  design  of  outlet  works  vary  with  the  type 
of  dam.  The  outlet  gates  for  a  masonry  dam  are  usually  located 
on  the  upstream  face  or  a  short  distance  inside  the  face.  Some- 
times they  are  located  in  a  tunnel  running  around  the  dam.  The 
latter  method  is  preferable  where  practicable.  Earth  and  rock- 
fill  and  other  dams  having  flat  slopes  require  the  construction 
of  an  outlet  tower  in  which  the  operating  gates  are  locatecl,  and 


WORKING  DATA  FOR   IRRIGATION  ENGINEERS 


TABLE   13 
MAXIMUM  RATE  OF  DISCHARGE  OF  STREAMS  IN  THE  UNITED  STATES  * 


Stream  and  Place 

Drainage 
Area, 
Sq.  Miles 

Date 

Cu.  Ft.  per 
Sec.  per 
Sq.  Mile 

Budlong  Creek,  Utica,  N.  Y  

1.13 

1904 

12040 

Sylvan  Glen  Creek,  New  Hartford,  N.  Y  .  . 
Pequest  River,  Hunts  Pond,  N.  J  
Starch  Factory  Creek,  New  Hartford,  N.  Y. 
Starch  Factory  Creek,  New  Hartford,  N.  Y. 
Reels  Creek,  Deerfield,  N.  Y  

1.18 
1.70 
3.40 
3.40 
4.40 

1904 
1904 
1904 
1905 
1904 

56.58 
25.30 
109.62 
209.00 
4836 

Mad  Brook,  Sherburne,  N.  Y  

5.00 

1905 

26200 

Skinner  Creek,  Mannsville,  N.  Y  

6.40 

1891 

124.20 

Coldspring  Brook,  Mass 

643 

1886 

48  40 

Croton  River,  South  Branch,  N.  Y  
Woodhull  Reservoir,  Herkimer,  N.  Y  
Mill  Brook,  Edmeston,  N.  Y  

7.80 
9.40 
9.40 

1869 
1869 
1905 

73.90 

77.80 
241  00 

Stony  Brook,  Boston,  Mass  

12.7 

121.00 

Great  River  Westfield   Mass 

140 

71  40f 

Smartswood  Lake,  N.  J 

160 

68  00 

Williamstown  River,  Williamstown,  N.  Y  .  . 
Croton  River,  West  Branch,  N.  Y 

16.5 
20.5 

1874 

34.00 
5440 

Beaverdam  Creek,  Altmar,  N.  Y  

20.7 

111  00 

Trout  Brook,  Centerville,  N.  Y  

23.0 

50.60 

Wantuppa  Lake,  Fall  River,  Mass  
Pequest  River   Huntsville  N   T 

28.5 
31  4 

1875 

72.00 
19  30 

Sawkill   near  mouth   N  J 

350 

22860 

Whippany  River,  Whippany,  N.  J  
Cuyadutta  Creek,  Johnstown,  N.  Y  

37.0 
40.0 

1903 
1896 

61.62 
72.40 

West  Canada  Creek,  Motts  Dam,  N.  Y  
Six  Mile  Creek,  Ithaca,  N.  Y  
Sauquoit  Creek,  New  York  Mills,  N.  Y  
Roc  ka  way  River  Dover,  N.  J 

47.5 
47.5 
51.5 
52.5 

i905 

34.10 
170.00 
53.40 
43  00 

Oneida  Creek,  Kenwood,  N.  Y 

59.0 

1890 

41  20 

Flat  River,  R.  I      .              

61.0 

1843 

120.00 

Camden  Creek,  Camden,  N.  Y  

61.4 

1889 

24.10 

Nine  Mile  Creek,  Stittville,  N.  Y.  ......... 
Wissahickon  Creek,  Philadelphia,  Pa  
Sandy  Creek,  Allendale,  N.  Y 

62.6 
64.6 
68.4 

1898 
1898 
1891 

124.90 
43.50 
87.70 

Rock  Creek,  Washington,  D.  C  

77.5 

126.30 

Sudbury  River,  Farmington,  Mass  

78.0 

1897 

41.38 

Peouanock  River   Pompton   N  J 

780 

1902 

5578 

Hockanum  River,  Conn  

79.0 

78.10 

Nashua  River   Mass 

84.5 

1850 

71.04 

Independence  Creek,  Crandall,  N.  Y  
Passaic  River,  Chatham,  N.  J  

93.2 
100 

1869 
1903 

66.50 
17.20 

Deer  River,  Deer  River,  N.  Y  

101 

1869 

78.10 

Wanaque  River,  N.  J  
Tohickon  Creek,  Mount  Pleasant,  Pa  

101 
102 

1882 
1885 

66.00 
112.50 

Fish  Creek,  East  Branch,  Point  Rocks,  N.  Y. 
Nashua  River,  Mass 

104 
109 

1897 

1848 

80.50 
104.53 

Sandy  Creek,  North  Branch,  Adams,  N.  Y  . 
Scantic  River   North  Branch   Conn 

110 
118 

1897 

67.30 
51.80 

Ramapo  River,  Mahawah,  N.  J  

118 

1903 

105.09 

*From  "American  Civil  Engineers'  Pocket  Book,"  John  Wiley  &  Sons,  New  York, 
t  Average  flow  for  day  of  maximum  discharge. 


DESIGN   OF   IRRIGATION   STRUCTURES 

TABLE   13  (Continued) 
MAXIMUM  RATE  OF  DISCHARGE  OF  STREAMS  IN  THE  UNITED  STATES 


35 


Stream  and  Place 

Drainage 
Area, 
Sq.  Miles 

Date 

Cu.  Ft.  per 
Sec.  per 
Sq.  Mile 

Rockaway  River   Boonton   N.  J 

125 

1902 

2224 

Patuxent  River  Laurel   Md 

137 

1897 

31  20 

Meshaminy  Creek,  below  forks,  Pa  
Oriskany  Creek,  Colemans,  N.  Y  
Oriskany  Creek  Oriskany,  N.  Y  

139 
141 
144 

1894 
1888 
1904 

97.60 
55.80 
2900 

Perkiomen  Creek,  Frederick,  Pa  
Mohawk  River   Ridge  Mills,  N.  Y  

152 
153 

1889 

69.20 
4640 

Mohawk  River,  State  dam,  Rome,  N.  Y.  .  . 
Ramapo  River,  Pompton,  N.  J  .          

158 
160 

1904 

1882 

27.34 
56  10 

Fish  Creek,  W.  B.,  McConnellsville,  N.  Y.  . 
Unadilla  River,  New  Berlin,  N.  Y  
Salmon  River,  Altmar,  N.  Y  

187 
204 
221 

1885 
1905 

32.70 
40.00 
27.60 

Black  River,  Forestport,  N.  Y  
Croton  River,  Croton  Dam,  N.  Y  
Great  River,  Westfield,  Mass  

268 
339 
350 

39.00 
74.40 
151.90 

East  Canada  Creek,  Dolgeville,  N.  Y  
Moose  River  Ayers  Mill   N   Y 

356 
407 

1898 

24.70 
31  00 

Stony  Creek,  Johnstown,  Pa  

428 

70.00 

West  Canada  Creek,  Middleville,  N.  Y.  .  .  . 
Farmington  River   Conn 

518 

584 

1898 

24.90 
41  70 

Monocacy  River,  Frederick,  Md  
Passaic  River,  Little  Falls,  N.  J  
North  River,  Port  Republic,  Va  
Passaic  River,  Dundee,  N.  Y 

665 
773 

804 

823 

1898 
1882 
1896 
1903 

29.80 
24.20 
29.80 
43  38 

North  River,  Glasgow,  Va 

831 

1896 

4480 

Raritan  River,  Boundbrook,  N.  J 

879 

1882 

5930 

Potomac,  North  Branch,  Cumberland,  Md. 
Black  River,  Lyons  Falls,  N.  Y  

891 

897 

1897 
1869 

22.80 
4600 

Schoharie  Creek,  Fort  Hunter,  N.  Y  
Genesee  River,  Mount  Morris,  N.  Y  

Mohawk  River,  Little  Falls,  N.  Y  
Greenbrier  River,  Alderson,  W.  Va  
Black  River,  Carthage,  N.  Y  
Schuylkill  River,  Fairmount,  Pa  
Chemung  River,  Elmira,  N.  Y  
James  River,  Buchanan,  Va  

948 
1,070 

1,306 
1,344 
1,812 
1,915 
2,055 
2,058 

1892 
/  1894  \ 
\  1896  / 
1902 
1897 
1869 
1898 
1889 
1896 

44.00 
39.20 

21.83 
41.60 
21.20 
12.20 
67.10 
1560 

Androscoggin  River,  Rumford,  Me  

2,220 

1869 

25.00 

Genesee  River,  Rochester,  N.  Y  

2,365 

1865 

17.00 

Hudson  River,  Fort  Edward,  N.  Y 

2825 

1900 

15  60 

Shenandoah  River,  Millville,  W.  Va  ...... 
Mohawk  River,  Rexford,  N.  Y 

2,995 
3,384 

1898 
1892 

11.40 
23  10 

Merrimac  River,  Lowell,  Mass 

4,085 

19  80 

Kennebec  River,  Waterville,  Me 

4,410 

1896 

2520 

Susquehanna,  W.  Branch,  Williamsport,Pa. 
Hudson  River,  Mechanicsville,  N.  Y.    . 

4,500 
4,500 

i869 

11.60 
15  50 

Merrimac  River,  Lawrence,  Mass  .  .  . 

4,553 

23  40 

Potomac  River,  Dam  No.  5,  Md  

4,640 

22  20 

Delaware  River,  Lambertville,  N.  J  
Delaware  River,  N.  J 

6,500 
6  750 



53.80 
5000 

Delaware  River,  Stockton,  N.  J  
Susquehanna  River,  Northumberland,  Pa.  .  . 

6,790 
6,800 

1841 

1889 

37.59 
17.50 

36  WORKING  DATA  FOR   IRRIGATION   ENGINEERS 

TABLE   13  (Continued) 
MAXIMUM  RATE  OF  DISCHARGE  OF  STREAMS  IN  THE  UNITED  STATES 


Stream  and  Place 

Drainage 
Area, 
Sq.  Miles 

Date 

Cu.  Ft.  per 
Sec.  per 
Sq.  Mile 

Connecticut  River  Holyoke,  Mass  .  .  . 

8,660 

1854 

21  10 

Potomac  River,  Point  of  Rocks,  Md  
Connecticut  River,  Hartford,  Conn  
Potomac  River  Md 

9,654 
10,234 
11  043 

1897 

19.40 
20.30 
4260 

Potomac  River,  Great  Falls,  Md  
Potomac  River  Chain  Bridge  D.  C  . 

11,427 
11  545 

1889 
1893 

41.20 
1720 

Susquehanna  River,  Harrisburg,  Pa  
Coosawattee  River,  Carters,  Ga  
Etowah  River,  Canton,  Ga  
Tuckasegee  River,  Bryson,  N.  C  

24,030 
532 
604 
662 

1894 
1901 
1895 
1899 

18.90 
31.86 
31.50 
58.23 

Little  Tennessee  River,  Judson,  N.  C  
Broad  River  Carlton  Ga 

675 
762 

1901 
1902 

85.24 
3822 

Saluda  River  Waterloo,  S.  C  .  .  . 

1,056 

1903 

1800 

Catawba  River,  Catawba,  N.  C  
Chattahoochee  River,  Oakdale,  Ga  
Ocmulgee  River,  Macon,  Ga  

1,535 
1,560 
2,425 

1901 
1899 
1902 

53.10 
27.92 
20.97 

Yadkin  River  Salisbury  N.  C 

3399 

1899 

'    31  60 

Tallapoosa  River,  Milstead,  Ala  
Coosa  River  Rome,  Ga  ... 

3,840 
4,001 

1901 
1901 

18.23 
1604 

Broad  River,  Alston,  S.  C  .  .  . 

4,609 

1901 

28.44 

Black  Warrior  River,  Tuscaloosa,  Ala  
New  River,  Fayette,  W.  Va  

4,900 
6,200 

1900 
1899 

27.89 
17.83 

Coosa  River,  Riverside,  Ala  
Savannah  River  Augusta,  Ga 

6,850 
7294 

1898 
1888 

10.53 
42  50* 

Tennessee  River,  Chattanooga,  Tenn  
Des  Plaines  River,  Riverside,  111  

21,418 
630 

1896 
1892 

20.80 
905* 

Verdigris  River,  Liberty,  Kans  
Neosho  River,  tola,  Kans  

3,067 
3,670 

1904 
1904 

16.43 
20.33 

Grand  River,  Grand  Rapids,  Mich  
Smoky  Hill  River  Ellsworth,  Kans 

4,900 
7980 

1905 
1903 

10.00 
1  43* 

Kanawha  River,  Charleston,  W.  Va. 

8,900 

1875 

13  50 

Blue  River,  Manhattan,  Kans  
Republican  River,  Junction,  Kans  
Mississippi  River,  St.  Paul,  Minn  
Kansas  River,  Lecompton,  Kans  

9,490 
25,837 
36,085 
58,550 

1903 
1903 
1897 
1903 

7.25* 
1.80* 
19.70 
3.98 

Gallinas  River  Las  Vegas,  N.  Mex 

90 

1904 

129  10 

Mora  River,  La  Cueva,  N.  Mex 

159 

1904 

13970 

Rapid  Creek,  Rapid,  S.  Dak  

320 

1904 

2.85 

Salt  Creek,  at  mouth,  N.  Mex  
Hondo  River,  reservoir,  N.  Mex  
Canadian  River,  Logan,  N.  Mex  

3,052 
1,387 
11,440 

1904 
1904 
1904 

4.10 
4.56 
12.29  a 

Canadian  River,  Taylor,  N.  Mex  
Canadian  River,  French,  N.  Mex 

2,832 
1,478 

1904 
1904 

32.11  b 
105.56  c 

Pecos  River,  Fort  Sumner,  N.  Mex  
Pec(fs  River,  Roswell,  N.  Mex  
Redwater  River,  Belle  Fourche,  S.  Dak  
Sapello  River,  Los  Alamos,  N.  Mex  

6,191 
14,840 
1,006 
221 

1904 
1904 
1904 
1904 

7.29 
3.75 
8.00 
36.7 

Purgatory  River,  Trinidad,  Colo  
Salt  River,  Roosevelt,  Ariz  

742 
5,756 

1904 
1893 

61.2 
36.0 

Verde  River,  McDowell,  Ariz  

6,000 

1893 

24.05  d 

*  Average  flow  for  day  of  maximum  discharge. 

a,  Rate  for  12  hours,    b,  Rate  for  7  hours,    c,  Rate  for  0.5  hour,    d,  Rate  for  24  hours. 


DESIGN   OF   IRRIGATION   STRUCTURES 


37 


TABLE    13  (Concluded] 
MAXIMUM  RATE  OF  DISCHARGE  OF  STREAMS  IN  THE  UNITED  STATES 


Stream  and  Place 

Drainage 
Area, 
Sq.  Miles 

Date 

Cu.  Ft.  per 
Sec.  per 
Sq.  Mile 

Salt  River,  Ariz  
Gila  River,  Florence,  Ariz  
Pecos  River  Santa.  Rosa  N  Mex 

12,000 
17,750 
2,649 

1891 

1891 
1904 

24.69 
7.50 
17.56 

Mora  River  Weber  N.  Mex 

422 

1904 

65.70 

Rio  Grande,  Rio  Grande,  N.  Mex  
Yuba  River,  Bowman  Dam,  Cat  
Sweet  water  River,  Sweetwater  Dam,  Cal  .  . 
Tuolumne  River,  Lagrange,  Cal  
San  Joaquin  River,  Hamptonville,  Cal  .... 
King  River,  State  Point,  Cal  
Kern  River,  Rio  Bravo,  Cal  
Sacramento  River,  Iron  Canon,  Cal  
Yuba  River,  Smartsville,  Cal  
Feather  River,  Oroville,  Cal  
Stony  Creek,  Fruto,  Cal  

11,250 
19 
186 
1,501 
1,637  . 
1,742 
2,345 
9,295 
1,220 
3,350 
760 

1904 
1895 

1881 
1901 
1897 
1904 
1904 
1904 
1904 

2.75 
31.6    • 
97.5 
30.6 
36.51f 
25.22 
2.3f 
23.47  f 
49.02f 
31.49t 
29.21f 

t  Mean  for  day  when  discharge  was  a  maximum. 

a  discharge  conduit  running  through  or  around  the  dam.  In 
this  case,  also,  the  latter  method  is  preferable  where  practicable. 
The  gates  and  conduits  must  be  designed  to  pass  the  required 
quantity  of  water  at  low  as  well  as  high  heads  corresponding  to 
the  fluctuations  in  the  elevation  of  the  reservoir  water.  To  avoid 
the  necessity  of  operating  the  gates  at  very  high  heads  they  are 
sometimes  located  at  several  levels,  the  upper  ones  being  used 
when  the  water  is  high  and  the  lower  ones  when  the  water  is  low, 
the  water  from  the  higher  levels  either  shooting  directly  through 
the  dam,  in  the  case  of  a  masonry  dam,  or  dropping  down  a 
shaft  in  the  outlet  tower  and  thence  through  the  outlet  conduit, 
in  the  case  of  other  dams.  For  high  heads,  ordinary  slide  gates 
are  not  suitable  on  account  of  the  difficulty  of  operation  and 
destructive  effect  of  vibrations  due  to  high  velocities.  For  this 
purpose,  some  form  of  balanced  cylindrical  or  needle  valve  is 
necessary.  The  use  of  a  single  gate  is  seldom  advisable,  but  there 
should  be  two  gates  in  series  at  each  outlet,  so  that  one  will  be 
supplemented  by  the  other,  and  in  case  of  damage  to  either  the 
other  can  be  used  for  regulation.  This  arrangement  is  imperative 
where  the  gates  are  to  be  submerged,  and  consequently  inac- 
cessible, for  long  periods  of  time. 


38  WORKING  DATA  FOR  IRRIGATION   ENGINEERS 

In  all  forms  of  gates  and  valves,  air  should  have  free  access 
to  the  chamber  on  the  downstream  side  of  the  gate  to  prevent 
the  periodic  formation  and  release  of  a  partial  vacuum,  which  is 
so  destructive  to  gates.  Where  the  partial  vacuum  can  be  main- 
tained at  all  stages  of  flow  it  will  have  no  more  destructive  effect 
than  that  due  to  the  increased  velocity  produced,  but  this  is 
not  usually  the  case. 

High  velocities  flowing  smoothly  have  very  little  destructive 
effect  on  concrete  (see  page  47),  but  a  smooth  flow  is  seldom 
obtained  in  the  outlet  conduit  of  a  reservoir.  To  protect  the 
concrete,  conduits  are  sometimes  lined  with  cast  iron  or  semi- 
steel,  the  latter  being  used  on  account  of  its  hardness  and  con- 
sequent resistance  to  erosion. 

Diversion  Dams. — There  are  two  general  types  of  diversion 
dam:  those  on  impervious  foundation  and  those  on  more  or  less 
pervious  foundations.  These  in  turn  may  each  be  subdivided 
into  fixed  crest  dams  and  movable  dams.  A  movable  crest  is 
necessary  where  a  fixed  crest  of  the  required  height  would  cause 
the  backwater  to  flood  the  country  excessively  during  periods  of 
high  water,  the  movable  crest  being  removed  from  the  path  of 
the  water  to  allow  the  flood  to  pass.  The  minimum  length  of 
dam  will  generally  be  roughly  fixed  by  the  topographic  conditions 
at  the  site,  and  the  height  to  which  the  water  must  be  raised  is 
fixed  by  the  elevation  of  the  irrigable  land  which  it  is  desired  to 
reach.  It  is  very  desirable  that  a  movable  dam  be  avoided,  if 
possible,  as  good  dams  of  this  kind  are  generally  expensive  to 
build,  as  well  as  to  operate  and  maintain.  After  the  maximum 
probable  flood  in  the  river  has  been  estimated,  high-water  marks 
have  been  located,  and  the  required  elevation  of  diversion  and 
length  of  dam  preliminarily  fixed,  calculations  must  be  made  of 
the  effect  at  high  water  of  damming  the  river  with  a  fixed  crest 
dam  to  raise  the  water  to  the  diversion  elevation  at  low  water. 
The  water  will  obviously  be  raised  higher,  due  to  this  artificial 
obstruction,  than  it  flowed  before,  and  this  effect  will  extend  up- 
stream an  indefinite  distance.  In  the  case  of  a  rapidly  flowing 
stream  confined  between  high  banks,  backing  up  the  water  may 
do  no  damage  to  lands  upstream,  but  in  case  the  opposite  con- 
ditions obtain,  the  effect  of  damming  up  the  water  even  a  small 


DESIGN   OF  IRRIGATION   STRUCTURES  39 

amount  might  prove  disastrous.  In  the  latter  case  there  may  be 
two  solutions:  the  length  of  the  dam  may  be  increased  or  a 
movable  crest  may  be  used.  It  will  generally  be  necessary  to 
make  many  detail  calculations  before  the  proper  adjustment  is 
reached.  The  principal  hydraulic  calculations  to  be  made  in 
this  connection  are  the  determination  of  the  depth  of  flow  over 
the  crest  and  the  elevation  of  backwater  at  various  points  up- 
stream. With  the  aid  of  Tables  28,  28  A,  28  B,  and  28  C  the 
depth  of  flow  may  be  determined  for  various  types  of  crest.  If 
the  determination  of  exact  depth  of  flow  is  of  great  importance  due 
to  probable  damage  from  backwater,  it  is  well  to  select  a  type  as 
close  as  possible  to  one  for  which  definite  coefficients  are  given. 

Exact  backwater  elevations  are  very  difficult  to  determine, 
as  theoretical  calculations  fail  almost  entirely  here.  It  is 
necessary  that  cross-sections  of  the  stream  be  obtained  at 
various  points,  and  the  slope  of  the  stream,  and,  if  possible, 
the  value  of  "  n  "  in  Kutter's  formula  determined;  if  this  can 
not  be  experimentally  determined,  it  must  be  assumed.  After 
the  foregoing  data  are  obtained,  the  loss  of  head,  or  drop  in 
water  surface,  of  the  stream  is  calculated  in  successive 
short  reaches  by  means  of  the  formula  Q  =  A  C  V  R  S.  The 
total  drop  from  any  point  upstream,  calculated  in  this  manner, 
added  to  the  maximum  elevation  of  the  water  surface  at  the 
dam  gives  the  elevation  of  flood  water  at  the  point  in  question. 
This  is  a  method  of  successive  approximation,  but  may  be 
depended  upon  to  give  more  exact  results  than  any  backwater 
formula  based  on  theoretical  considerations  only. 

If  a  movable  crest  dam  is  used,  the  determination  of  depth 
of  flow  over  the  fixed  crest  need  not  be  so  exact,  as  a  certain 
margin  of  safety  can  be  applied  in  the  height  of  the  movable 
portion.  For  example:  if  the  calculations  show  that  a  movable 
crest  5  feet  high  is  required,  then  absolute  safety  may  be  assured 
by  making  this  5J^  or  6  feet,  and  this  will  add  relatively  little 
to  the  expense. 

Diversion  dams  located  on  pervious  foundations — as  many 
diversion  dams  are — must  be  designed  to  withstand  a  certain 
amount  of  upthrust,  and  it  is  usually  assumed  that  this  varies 
from  the  maximum  hydraulic  head  at  the  heel  to  zero  or  a  small 


40  WORKING  DATA  FOR  IRRIGATION   ENGINEERS 

amount  at  the  toe,  or  at  such  point  as  the  water  has  egress  from 
under  the  downstream  apron  of  the  dam.  The  unit  upward 
pressure  at  any  point  is  equal  to  the  distance  of  that  point  from 
the  heel  of  the  dam  divided  by  the  total  length  of  the  path  of 
percolation,  multiplied  by  the  depth  of  the  water  upstream.  If 
there  are  cut-off  or  curtain  walls,  the  path  of  percolation  is 
assumed  to  follow  around  those  walls.  For  example,  the  accom- 
panying figure  represents  a  dam  subjected  to  a  maximum  head 


of  water  above  0  equal  to  H.  It  is  assumed  that  the  pressure  of 
the  water  percolating  under  the  dam  reduces  to  zero  at  E. 
B  C  represents  an  impervious  curtain  wall,  and  the  path  of  per- 
colation is  O  A  B  C  D  E.  The  upward  pressure  at  B,  then,  is 

equal  to  n  .  ~r  n  ,.,  ;  similarly  the  pressure  at  D  is  equal  to 
\J  A.  Jj  C  L)  Hi 


IT  vx    r\  -p 

r\  A  g  r  n  *?•  **  *s  obvious  that  the  longer  the  apron  A  B 
DA.  jj  \s  L)  Hi 

and  the  curtain  wall  B  C  are  made,  the  lighter  may  the  cross- 
section  of  the  dam  be,  and  calculations  should  be  made  to  deter- 
mine what  is  the  most  economical  arrangement.  The  upthrust 
pressures  must,  of  course,  be  combined  with  the  usual  horizontal 
and  vertical  pressures  of  water  and  masonry  to  determine  the 
Stability  of  the  dam. 

Headgates.  —  In  a  stream  that  does  not  carry  much  silt,  the 
headgates  may  be  built  perpendicular  to  the  direction  of  flow  of 
the  stream,  but  in  streams  which  do  carry  much  silt,  it  will 
generally  be  necessary  to  build  the  headgates  parallel,  or  nearly 
parallel,  to  the  stream,  and  provide  a  sluicing  channel  through 
the  dam  in  front  of  them  in  order  to  allow  the  periodic  washing 
out  of  the  channel;  otherwise,  large  quantities  of  silt  would 


DESIGN   OF   IRRIGATION   STRUCTURES  41 

necessarily  have  to  be  carried  into  the  canal.  The  velocity 
through  headgates  must  generally  be  held  to  a  comparatively 
low  figure  to  avoid  heavy  washing  in  the  canal  or  the  necessity 
of  expensive  paving  and  other  protective  works  for  long  dis- 
tance downstream. 

In  some  cases  it  is  necessary  to  protect  the  gate  openings 
with  a  grillage  or  screen  to  keep  large  floating  debris  from  enter- 
ing the  canal.  In  other  cases,  a  simple  shear  boom  is  sufficient, 
but  this  does  not  keep  out  material  rolling  along  the  bottom  or 
carried  in  suspension.  The  kind  and  amount  of  protection 
depend  entirely  upon  the  nature  of  the  stream  and  the  location 
of  the  headworks  relative  to  it.  In  streams  in  which  fish  abound, 
State  laws  sometimes  require  that  a  fish  screen  be  placed  in 
front  of  the  gates  to  keep  the  fish  from  going  down  the  canal. 
A  satisfactory  screen  for  this  purpose  has  never  been  devised, 
the  great  difficulty  being  that  in  order  to  be  effective  in  stopping 
the  progress  of  the  fish  the  mesh  of  the  screen  must  be  so  small 
(from  one-fourth  to  one-half  inch)  that  the  screen  soon  becomes 
clogged  and  interferes  seriously  with  the  regulation  of  water 
through  the  gates.  The  heavy  expense  of  continually  cleaning 
such  a  screen  is  obvious,  and  even  then  it  is  very  difficult  to  keep 
a  constant  quantity  of  water  flowing  through  the  gates;  the  result 
is  that  the  use  of  fish  screens  is  not  very  popular. 

Canals. — The  determination  of  the  most  economical  design 
for  a  canal  is  one  of  the  most  difficult  problems  with  which  the 
irrigation  engineer  has  to  deal,  and  there  are  many  problems 
that  must  be  considered.  It  is  the  purpose  here  to  point  out 
the  most  important  of  these  problems  and  the  methods  of 
solution. 

Capacity. — It  is  assumed  that  the  engineer  has  before  him  a 
map  showing  the  preliminary  location  of  the  main  canal  and  the 
area  to  be  irrigated.  It  is  also  assumed  that  it  has  been  pre- 
liminarily determined  at  what  points  the  principal  laterals  will 
divert  from  the  main  canal  and  the  approximate  areas  they  will 
irrigate.  These  points  are  marked  on  the  map,  together  with 
the  length  of  canal  between  them.  The  problem  of  capacity  of 
canal  at  any  point  now  involves  the  determination  of  the  duty 
of  water,  or  the  amount  required  to  be  applied  to  the  land,  and 


42 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


the  determination  of  losses  by  seepage  in  the  distribution  laterals 
and  main  canal  itself.  The  duty  of  water  is  discussed  on  page  20. 
For  the  purposes  of  main-canal  design,  the  losses  in  the  distri- 


bution  system  may  be  taken  as  15  per  cent  of  the  quantity 
diverted  from  the  main  canal. 

In  determining  capacities  it  is  convenient  to  begin  at  the 
lower  end  of  the  canal  and  work  up,  following  through  the  same 
calculations  for  each  successive  reach.  As  an  example:  Suppose 
the  accompanying  figure  represents  the  lower  end  of  a  canal; 
large  laterals  are  to  be  taken  out  at  points  B  and  C.  The  duty 
of  water  (quantity  applied  to  land)  has  been  decided  to  be 
2  acre-feet  per  acre  per  season;  the  irrigation  season  is  184  days 
long;  the  maximum  capacity  of  canal  required  in  mid-summer  is 
25  per  cent  greater  than  the  average;  the  velocity  to  be  used 
is  2.5  feet  per  second;  the  loss  by  seepage  from  the  main  canal 
is  1.5  feet  in  depth  over  the  wetted  area  per  day: 

The  duty  of  2  acre-feet  per  acre  in  a  season  of  184  days  cor- 
responds to  a  flow  of  1  c.  f .  s.  to  182  acres.  The  lower  reach  of 
the  main  canal  B  A  is  nothing  more  than  a  lateral,  and  it  will 
be  included  with  lateral  N  to  give  a  total  acreage  just  above  B 
of  3,000  acres.  At  1  c.  f.  s.  to  182  acres  applied  to  the  land  and 
with  a  loss  by  seepage  in  the  laterals  of  15  per  cent  of  the  diver- 
sions, the  required  maximum  discharge  of  main  canal  at  B  is 

3000X1.25 

, .  =  24.2  c.  f.  s.    If  there  were  no  seepage  losses 

lo^  /\   (^1  —  O.LO) 

the  capacity  at  C  would  be  the  same  as  at  B  as  no  laterals  di- 
vert from  the  canal  between  these  points.  To  determine  the 
loss  by  seepage,  assume  the  average  flow  in  the  reach  C  B  to 


DESIGN   OF   IRRIGATION   STRUCTURES  43 

be  25  c.  f  .  s.  ;  enter  the  diagram,  Fig.  3,  with  Q  =  25  as  an 
argument  and  find  where  this  line  intersects  the  inclined 
line  marked  C  =  1.5,  and  read  the  seepage  loss  =  1.5  c.  f.  s. 
per  mile  on  the  scale  to  the  left  for  V  =  1  and  for  V  =  2.5 
follow  the  diagonal  line  to  the  left  to  its  intersection  with  the 
vertical  line  marked  V  =  2.5  and  read  the  seepage  loss  for  the 
case  in  hand  to  be  0.95  c.  f.  s.  per  mile,  or  1.9  c.  f.  s.  for  the  two 
miles  from  C  to  B.  The  required  capacity  at  C  then  is  24.2  + 
1.9  =  26.1  c.  f.  s.  This  process  is  now  repeated  for  each  suc- 
cessive reach  above  C  until  the  head  of  the  main  canal  is  reached. 
Seepage  Losses.  —  For  convenience,  losses  by  seepage  have 
frequently  been  expressed  in  terms  of  the  percentage  of  water 
lost  per  mile,  or  other  unit  of  length.  This  method  is  absolutely 
irrational  and  fortunately  is  rapidly  falling  into  disuse,  except 
for  very  general  statements.  The  most  rational  and  convenient 
means  of  stating  these  losses  is  in  terms  of  the  number  of  feet 
in  depth  over  the  wetted  area  of  the  canal  prism  lost  in  one  day. 
The  following  formula*  has  been  deduced  for  seepage  loss: 


Where   5  =  loss  in  c.  f.  s.  per  mile  of  canal, 
Q  =  discharge  of  canal  in  c.  f.  s., 
V  =  mean  velocity  of  flow  in  feet  per  second, 
C  =  the  depth  in  feet  over  the  wetted  perimeter 

lost  per  day,  and  is  found  from  observation 

on  existing  canals. 

An  exact  expression  for  seepage  loss  involves  the  depth  of 
flow,  inclination  of  side  slopes,  and  the  ratio  of  depth  to  bottom 
width,  but  it  is  mathematically  demonstrated  in  the  article 
above  referred  to  that  the  above  formula  which  is  based  on  side 
slopes  of  1  J^  to  1  and  a  bottom  width  of  four  times  the  depth, 
gives  results,  for  any  shape  or  proportions  of  section,  that  are 
well  within  the  limit  of  accuracy  of  the  data  which  it  is  necess- 
ary to  use  in  connection  therewith. 

Observations  on  several  hundred  miles  of  earth  canals  on 

*  See  Engineering  News,  Vol.  LXX,  page  402,  for  the  derivation  of  this 
formula  and  a  discussion  of  seepage  losses. 


44  WORKING  DATA   FOR   IRRIGATION   ENGINEERS 

eight  different  projects  of  the  United  States  Reclamation  Service 
give  the  following  average  figures  for  the  value  of  C: 

TABLE   14 
SEEPAGE   LOSSES  FROM   CANALS  IN  VARIOUS   MATERIALS 


Kind  of  Material 

No.  of 
Observations  | 

Loss 

Cement  gravel  and  hardpan  with  sandy  loam  

3 

0.34 

Clay  and  clay  loam 

5 

0  41 

Sandy  loam  .  .        

4 

0  66 

Volcanic  ash  

3 

0  68 

Volcanic  ash  with  some  sand  

5 

0  98 

Sand  and  volcanic  ash  or  clay  

8 

1  20 

Sandy  soil  with  some  rock 

3 

1  68 

Sandy  and  gravelly  soil  ....           *     .            ... 

8 

2  20 

These  are  generally  results  from  canals  that  have  been  in 
operation  from  three  to  six  years.  There  is  usually  a  very 
noticeable  reduction  in  seepage  losses  with  continued  use,  es- 
pecially if  the  water  carries  fine  silt,  and  there  are  instances 
where  the  most  porous  gravel  formation  has  been  made  practi- 
cally watertight  by  a  coating  of  silt  or  puddle.  In  designing  a 
canal,  it  is  probably  unsafe  to  figure  on  a  smaller  loss  than 
0.5  foot  over  the  wetted  area  in  24  hours  in  even  the  most  imper- 
vious material,  and  after  a  loss  of  over  2  to  2.5  feet  is  reached  the 
question  of  lining  the  canals  will  generally  require  very  serious 
consideration  from  the  point  of  view  of  value  of  the  water  and 
damage  to  adjoining  lands  from  waterlogging.  The  limits 
within  which  seepage  losses  should  be  considered  may,  therefore, 
be  generally  defined  as  0.5  foot  and  2.5  feet  per  day  over  the 
wetted  area  of  canal,  for  the  minimum  and  maximum  respec- 
tively. 

The  manipulation  of  the  equation  is  made  very  simple  by 
the  use  of  Fig.  3,  which  gives  the  loss  by  seepage  in  cubic  feet, 
per  second  per  mile  of  canal  for  a  large  variety  of  conditions. 

Side  Slopes. — The  proper  slope  to  give  the  sides  of  a  canal 
depends  upon  the  stability  of  the  material.  .  Earth  canals  are 
generally  given  a  slope  of  1^  to  1  or  2  to  1,  and  these  may  be 
taken  as  the  standard  for  ordinary  conditions.  When  the 
channel  is  lined,  the  side  slopes  may  be  made  of  any  inclination 


DESIGN   OF   IRRIGATION   STRUCTURES 


45 


Jt 

-\ 

\ 

\ 

S 

\ 

^ 

\ 

^ 

^ 

\ 

\ 

V 

\ 

C~ 

\ 

*i 

o 
* 

jT 

V 

\ 

\> 

\ 

\ 

\ 

\ 

\ 

\ 

\ 

s. 

4 

L 

\     * 

^ 

0 

\ 

^V 

x~ 

s 

)\ 

o\ 

3 

5 

9 

\ 

\ 

\ 

\ 

s 

\ 

\ 

\ 

\ 

\ 

I 
1 

-  -5 

^ 

^~ 

^V 

\ 

V 

§         " 

s. 

S 

\ 

O       i^-* 

\ 

\ 

»3    c 

\ 

\ 

^ 

\ 

\ 

\ 

^                  ^ 

\ 

\ 

\ 

\ 

^           \ 

\ 

\ 

\ 

\ 

\ 

V 

\ 

\ 

y 

\ 

0         % 

\ 

V 

^     O 

V 

^ 

\ 

s. 

\           ^ 

\ 

o     0 

\ 

\      v 

\ 

\ 

\ 

\ 

\ 

o      t? 

\ 

\ 

\ 

\ 

0       KJ 

\ 

\ 

\ 

0       ° 

\ 

\ 

o     •% 

V  \ 

^ 

> 

\ 

\ 

c 

>l> 

\    \ 

\ 

\ 

\ 

\ 

* 

0 

-tn1- 

§ 

\ 

\ 

\ 
\ 

\ 

i 

M 

s::::^_ 

S; 

^ 

\ 

-V 

M 

^ 

i 

\ 

\ 

\ 

^ 

^ 

^ 

\ 

\ 

\ 

\ 

\^ 

s 

i   o 

o     < 

e 

<: 

<3 

i       >i 

i 

, 

\ 

vq 

\ 

CO       r 

'J 

* 

C9         3J 

2.        ^ 

" 

« 

\^ 

\ 

0 

V\ 
\ 

\ 
\ 
\ 

\ 
\ 

\ss 

\s\ 

Sss 

\ 
\ 
\ 

\ 
\ 

\ 

\ 
\ 

\ 
^\ 

\ 
\ 

\ 
\ 

\ 

\ 

S!!!|i 

11 

\ 
\ 

\ 
\ 
\ 

\ 
\ 

V 

\^ 
\ 

\^ 

\ 

\ 
\ 

\ 
\ 

\ 
\ 

\ 

\ 

\ 

fi'T  -H 

S 

\  \ 

s^ 

\ 
\ 

\ 
\ 

J\ 

.  s 
\ 

\ 

s 

.  \ 

\\Y 

SSsw^    \ 
\ss^V    V 

X 
\ 

\ 
\ 

\ 
\ 

X 
\ 

\ 

\ 

^s 

A 

;\ 

^  \ 

s  > 

:   v  \ 

Sj 

A 
\ 

^ 

X\ 
, 

s\ 

\s 

s\ 

v  s\s 

sl^^ 

\ 
\ 

^y 

\ 

\ 
v 

^ 

\ 

\ 

\j 

s\ 

' 

S\\ 

\ 

s 

sN 

\\ 

S 

\ 

\N 

s  \  v 

\    S    § 

^ 

^ 

V 

V 

\> 

s^> 

v\ 

5 

^ 

\\ 

Y 

N\i 

? 

5? 

3     = 

' 

c 

c 

s 

C 

3     '.1 

5 

\f 

I 

c 

> 

! 

anK  jad  ^oa^-puooeg  m  ssoi  8St?doos=s 
FIG.  3. — Diagram  for  Use  in  Calculating  Seepage  Losses  in  Canals. 


46  WORKING   DATA   FOR   IRRIGATION  ENGINEERS 

up  to  vertical.  On  steep  side-hill  locations  the  slope  on  the  hill- 
side is  often  made  steeper  than  the  other  slope  in  order  to  avoid 
excessive  excavation.  Usually  no  difference  is  made  between 
the  side  slopes  in  cut  and  those  in  fill. 

Depth  of  Flow  and  Bottom  Width. — The  depth  and  bottom 
width  of  a  canal  section  are  obviously  interdependent.  It  has 
been  stated  that  the  maximum  depth  to  use  for  an  irrigation 
canal  in  earth  should  not  exceed  8  feet,  and  for  safety  and  econ- 
omy in  operation  it  is  probable  that  the  maximum  line  should  be 
fixed  at  10  feet,  except  for  uncommonly  large  canals.  It  is  very 
seldom  that  a  canal  is  designed  to  have  the  best  hydraulic  ele- 
ments, although  it  is  a  very  easy  matter  to  make  such  a  design. 
One  of  the  principal  reasons  for  this  is  that  the  most  efficient 
hydraulic  section  is  too  deep  for  its  width,  and  such  a  section 
will  not  keep  its  shape,  but  tends  to  broaden  and  become  more 
shallow.  In  rock  and  other  hard  material  and  for  lined  sections 
the  most  economical  section  can  generally  be  used. 

The  best  hydraulic  section  is  the  one  that  has  the  greatest 
hydraulic  radius  for  a  given  area;  such  a  section  may  be  picked 
out  by  inspection  from  Figs.  14  to  21.  For  example:  suppose  the 
channel  is  to  have  1  to  1  side  slopes;  the  required  area  of  cross- 
section  is  200  square  feet;  what  are  the  bottom  width  and  depth 
that  will  give  the  best  hydraulic  section?  Follow  the  line  (Fig.  16 
part  3)  marked  200  at  the  bottom  of  the  page  to  its  intersection 
with  the  bottom  width  that  gives  the  greatest  hydraulic  radius 
which  we  find  to  be  about  9  feet;  the  corresponding  depth  is 
10.3  feet;  and  the  hydraulic  radius  is  5.23.  In  case  of  a  rock 
or  lined  channel  this  section  could  be  used,  but  for  an  earth 
section  it  would  be  too  deep  for  its  width. 

The  best  ratio  of  bottom  width  to  depth  to  use  for  a  lined  or 
rock  section  is  usually  fixed  by  considerations  of  economy  only, 
but  for  canals  in  earth  the  depth  should  be  limited,  as  before 
stated,  to  about  8  or  10  feet,  although  canals  have  been  built 
with  greater  depths.  Ratios  of  bottom  width  to  depth  from  2  to  1 
to  6  to  1  are  commonly  used,  depending  largely  on  economy  of 
construction  and  operation.  Canals  in  materials  which  are 
easily  eroded  and  broken  down  require  the  greatest  relative 
bottom  widths. 


DESIGN   OF  IRRIGATION   STRUCTURES  47 

Velocities  and  Grades. — The  velocities,  and  correspondingly 
the  slopes,  for  concrete-lined  sections  are  practically  unlimited. 
Velocities  as  high  as  90  feet  per  second  have  been  used  on  con- 
crete without  destructive  effect,  but  such  velocities  are  not  to  be 
generally  recommended.  Velocities  of  20  to  30  feet  per  second 
are  common.  Mr.  A.  P.  Davis,  in  an  article  in  Engineering 
News  of  January  4,  1912,  sums  up  the  results  of  investigations 
of  the  safe  velocities  on  concrete  as  follows:  "  (1)  That  where 
clear  water  can  be  made  to  glide  over  concrete  without  disturbing 
its  velocity  or  abruptly  changing  its  direction,  there  is  no  practi- 
cal limit  to  the  velocities  that  can  be  permitted  without  harm. 
(2)  That  concrete  which  is  subjected  to  the  impact  of  water 
under  high  velocity  is  rapidly  eroded,  and  that  under  such  con- 
ditions the  velocities  must  be  very  carefully  limited."  In  rock 
sections,  unlined,  velocities  of  10  to  12  feet  are  not  of  ten  exceeded 
because  the  section  is  usually  so  rough  that  the  loss  of  head 
with  high  velocities  is  very  great;  and  also  because  many  rocks 
will  not  stand  a  higher  velocity  continuously. 

For  canals  in  earth  the  velocity  usually  varies  from  2  to  3 
feet  per  second.  Generally  speaking,  velocities  less  than  2  feet 
per  second  will  allow  the  deposition  of  silt  and  over  3  feet  per 
second  will  erode.  There  is  probably  not  a  canal  in  existence 
that  does  not  deposit  at  some  points  and  erode  at  others, 
even  though  the  material  be  identical.  The  best  velocity  to 
use  in  a  particular  material  is  not  subject  to  exact  mathemat- 
ical calculation.  The  mean  velocity  at  which  silt  will  deposit 
is  said  to  be  dependent  upon  the  depth  of  the  water,  which  is  no 
doubt  true.  It  is  a  well-known  fact  that  small  canals  erode  at  a 
lower  mean  velocity  than  large  canals.  It  is  probably  safe  to  say 
that  the  velocity  in  the  largest  canals  in  ordinary  earth  should 
not  exceed  3.5  feet  per  second  and  in  the  smallest  laterals  2 
feet  per  second,  and  that  the  minimum  velocities  should  be 
2  feet  and  1  foot,  respectively.  The  result  of  too  low  a  velocity 
is  not  only  to  deposit  silt,  but  the  growth  of  weeds  and  moss  is 
encouraged,  causing  the  channel  to  become  foul  and  require  fre- 
quent cleaning  to  maintain  its  capacity.  Of  the  two  evils  it  is 
better  to  build  a  canal  with  too  high  rather  than  too  low  a 
grade,  as  the  former  can  be  remedied  without  excessive  expense 


48  WORKING  DATA  FOR  IRRIGATION   ENGINEERS 

by  the  construction  of  checks,  while  the  latter  condition  is 
generally  impossible  to  correct  except  at  prohibitive  expense. 
In  some  canals,  checks  are  necessary  in  order  to  back  the  water 
up  to  the  high  turnouts  during  times  when  the  canal  may  be 
running  at  only  about  one-half  or  two-thirds  its  capacity.  This 
requirement  should,  however,  be  avoided,  if  possible,  by  locating 
the  turnouts  low  enough  to  take  out  their  proportional  quantity 
at  any  stage  of  the  mam  canal  flow. 

From  experiments  made  in  India,  Mr.  R.  S.  Kennedy  found 
that  the  velocity  at  which  neither  silting  nor  scouring  of  the 
canal  bed  will  occur  depends  upon:  (1)  the  depth  of  water  in 
the  canal,  (2)  the  character  of  the  silt,  and  (3)  the  quantity  of 
silt  carried  in  suspension.  The  experiments  indicated  that  the 
critical  velocity  varied  as  the  0.64th  power  of  the  depth  of  canal, 
and  the  equation  Vs  =  0.84  Z>'64  was  derived  for  water  fully 
charged  with  fine,  light  sandy  silt  brought  down  by  the  floods 
of  the  rivers  of  northern  India.  For  heavier  materials  the  coef- 
ficient 0.84  is  larger,  and  the  general  equation  then  is  Vs  = 
m  Z>'64.  Values  of  m  have  been  used  from  0.84  to  1.09,  as 
indicated  in  the  accompanying  table. 

The  equation  Vs  =  m  Z)'64  is  important  to  American  engi- 
neers principally  as  indicating  the  probable  variation  of  the 
scouring  velocity  with  the  depth  of  canal.  It  is  generally  agreed 
that  a  deep  canal  will  stand  a  higher  mean  velocity  than  a 
shallower  canal,  but  the  above  equation  is  probably  the  only 
attempt  that  has  been  made  to  express  this  phenomenon 
mathematically. 

It  is  difficult  to  say  how  closely  this  equation  fits  American 
canals,  but  it  is  probable  that  the  velocity,  Vs,  does  not  increase 
so  rapidly  with  increasing  depth.  For  canals  carrying  large 
quantities  of  silt  the  equation  may  give  the  true  conditions 
with  fair  accuracy,  but  for  canals  carrying  fairly  clear  water  the 
exponent  of  D  is  probably  smaller  and  is  probably  closer  to 
0.5  than  0.64.  The  critical  velocity  for  canals  carrying  fairly 
clear  water  would  then  be  Vs  =  m  D  °'5.  For  convenience  of 
comparison,  a  table  has  been  calculated  from  this  equation  also, 
as  it  probably  fits  the  conditions  on  American  canals  more 
closely  than  the  other.  It  certainly  agrees  better  with  Ameri- 


DESIGN   OF  IRRIGATION   STRUCTURES 


49 


TABLE   15 

CRITICAL  VELOCITY,  OR  MEAN  VELOCITY,  AT  WHICH  A  CANAL  WILL  NEITHER 

SILT  NOR  SCOUR 
Based  on  Kennedy's  formula  Vs  —  m  D0-64 

(For  silt-laden  waters) 


Depth  of 
Channel  in 

Fine,  Light, 
Sandy  Silt 

Somewhat  Coarser, 
Light,  Sandy  Silt 

Sandy,  Loamy 
Silt 

Rather  Coarse  Silt 
or  Debris 
of  Hard  Soils 

Feet 

D 

| 

m  =  0.84 

m  =  0.92 

m  =1.01 

m  =  1.09 

2 

1.30 

1.43 

1.56 

1.69 

2.5 

1.51 

1.66 

1.81 

1.96 

3 

1.70 

1.87 

2.04 

2.21 

3.5 

1.88 

2.07 

2.26 

2.44 

4 

2.04 

2.24 

2.45 

2.65 

4.5 

2.20 

2.42 

2.64 

2.86 

5 

2.35 

2.59 

2.82 

3.05 

5.5 

2.50 

2.75 

3.00 

3.25 

6 

2.64 

2.90 

3.17 

3.43 

7 

2.92 

3.21 

3.50 

3.80 

8 

3.18 

3.50 

3.82 

4.13 

9 

3.43 

3.77 

4.12 

4.46 

10 

3.67 

4.04 

4.40 

4.77 

11 

3.90 

4.29 

4.68 

5.07 

12 

4.12 

4.53 

4.94 

5.36 

TABLE   16 
CRITICAL  VELOCITY,  OR  MEAN  VELOCITY,  AT  WHICH  A  CANAL  WILL  NEITHER 

SILT  NOR  SCOUR 

Based  on  formula  Vs  =  m  D°-b 

(For  canals  carrying  fairly  clear  water) 


Depth  of 
Channel  in 

Fine,  Light, 
Sandy  Silt 

Somewhat  Coarser, 
Light,  Sandy  Silt 

Sandy,  Loamy 
Silt 

Rather  Coarse  Silt 
or  Debris 
of  Hard  Soils 

Feet 

D 

m  =*  0.84 

m  =0.92 

m  =  1.01 

m  =  1  .  09 

2 

1.18 

1.30 

1.42 

1.54 

2.5 

1.33 

1.46 

1.60 

1.73 

3 

1.45 

1.59 

1.75 

1.89 

3.5 

1.57 

1.72 

1.89 

2.04 

4 

1.68 

1.84 

2.02 

2.18 

4.5 

1.78 

1.95 

2.14 

2.31 

5 

1.88 

2.06 

2.26 

2.44 

5.5 

1.97 

2.16 

2.37 

2.56 

6 

2.06 

2.26 

2.47 

2.67 

7 

2.22 

2.44 

2.68 

2.89 

8 

2.38 

2.60 

2.86 

3.08 

9 

2.52 

2.76 

3.03 

3.27 

10 

2.66 

2.91 

3.20 

3.45 

11 

2.79 

3.05 

3.35 

3.62 

12 

2.91 

3.19 

3.50 

3.78 

NOTE:   This  table  is  based  on  general  hypotheses,  and  observation  of  American  canals 
unsupported  by  experiments. 


50  WORKING  DATA   FOR   IRRIGATION  ENGINEERS 

can  practice.     It  should  be  remembered  that  this  equation  is 
not  based  on  actual  experiments,  but  on  observation  only. 

Formula  for  Flow. — The  tables  and  diagrams  in  this  book  for 
designing  open  channels  are  based  on  the  Kutter  formula: 

-1— L  +  41.6  + 


4L6 


in  which  V  is  the  mean  velocity  in  feet  per  second;  R  is  the 
hydraulic  mean  radius;  S  is  the  "  slope  "  or  sine  of  the  angle  of 
inclination  of  the  water  surface;  and  n  is  an  empirical  coefficient 
varying  with  the  roughness  of  the  channel. 

The  formula  was  derived  from  experiments  mainly  on  river 
channels,  but  it  has  been  found  fairly  well  adapted  to  the  calcu- 
lation of  flow  in  all  open  channels,  and  the  value  of  n  has  been 
determined  for  a  large  variety  of  conditions.  For  artificial 
channels  the  value  lies  between  0.010  and  0.035  for  the  smoothest 
and  roughest  respectively.  The  value  for  earth  and  rock  sec- 
tions, unlined,  is  generally  considered  to  lie  between  0.020  and 
0.035,  and  for  lined  channels  between  0.010  and  0.015.  For  well- 
built  canals  in  earth  in  good  order  the  value  lies  between  0.020 
and  0.025,  the  lower  figure  being  applicable  to  the  more  compact 
materials  and  the  latter  for  lighter  materials  and  those  con- 
taining much  coarse  gravel.  The  value  0.0225  is  very  generally 
used  for  canals  in  earth.  The  value  of  n  for  rock  sections  de- 
pends very  largely  upon  the  amount  of  smoothing  off  that  is 
done.  With  the  amount  of  trimming  that  is  generally  done,  the 
value  probably  lies  between  .030  and  .035,  while  a  carelessly 
excavated  rock  channel  may  have  a  valve  as  high  as  0.040,  and 
a  very  smoothly  trimmed  channel  may  have  as  low  a  value  as 
0.025.  If  plenty  of  grade  is  available,  it  does  not  pay  to  smooth 
the  channel  up  much,  but  if  grade  is  valuable  it  may  prove  eco- 
nomical to  do  sufficient  trimming  to  bring  the  value  of  n  down 
to  .025.  The  values  .030  and  .035  are  in  general  use  for  rock 
sections. 

For  wood  flumes  or  wood-lined  channels  a  value  of  n  of  .012 
is  commonly  employed,  and  experience  seems  to  justify  this 


DESIGN   OF   IRRIGATION   STRUCTURES  51 

value.  For  concrete-lined  channels  n  =  .013  is  in  common  use. 
Experiments  seem  to  indicate  that  this  value  may  be  as  low 
as  .012  or  even  less  for  surfaces  built  against  forms  very  smoothly 
finished  with  a  steel  trowel,  while  surfaces  built  without  forms 
or  with  wood  forms  slightly  uneven  and  not  trowelled,  the 
value  is  probably  about  .014.  For  any  concrete  surface  reason- 
ably well  made,  .015  is  probably  the  upper  limit,  and  considering 
the  present  state  of  our  knowledge  of  the  subject  it  is  not  safe 
to  use  a  value  less  than  0.012. 

Less  is  known  in  regard  to  the  coefficients  for  steel  flumes 
than  for  any  other  form  of  lining,  but  sufficient  experiments  have 
been  made  to  indicate  that  the  value  is  probably  about  .015  for 
rough  joint  flumes  such  as  the  Maginnis  and  about  .012  for 
the  smoother  joint  flumes,  such  as  the  Hess  and  Hinman.  Some 
manufacturers  claim  values  as  low  as  .010  and  .011  for  their 
flumes,  but  there  is  not  sufficient  justification  for  the  use  of  a 
value  less  than  .012,  especially  since  steel  flumes  have  not  been 
in  use  long  enough  to  indicate  what  effect  age  may  have  on  their 
carrying  capacity.  The  accompanying  tables  *  give  the  results 
of  observations  on  concrete-lined  and  earth  channels  respectively, 
on  projects  of  the  United  States  Reclamation  Service.  These 
observations,  although  giving  largely  varying  results,  if  carefully 
analyzed,  indicate  that  the  values  .012  to  .014,  generally  used  for 
concrete  channels,  and  .020  to  .025,  for  earth  channels,  are  jus- 
tified. The  great  difficulty  of  measuring  the  slope  and  average 
velocity  accurately  explains  sufficiently  the  large  variations 
shown  in  the  table,  that  are  not  explained  by  differences  in  the 
condition  of  the  channel,  and  it  is  very  unlikely  that  more 
uniform  results  can  be  obtained  under  practical  conditions. 

On  account  of  the  great  uncertainties  existing  in  the  choice 
of  a  value  of  n,  it  is  very  desirable,  especially  for  structures  of 
great  importance,  to  know  what  the  hydraulic  conditions  would 
be  if  the  value  turned  out  to  be  something  other  than  assumed. 
For  example :  A  canal  is  under  design  in  a  material  which  it  is 
known  will  probably  erode  excessively  under  mean  velocities 
of  2.75  feet  per  second;  the  value  of  n  is  probably  not  less  than 

*  Taken  from  the  "Reclamation  Record,"  published  by  the  United  States  Reclamation 
Service. 


52 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


3 

i 

•c 

B 

£ 

"3 

g 

| 
•3 

w 
eu 
X 

c 

O 

O 

W 

* 

| 

"is 

B 

C 

£ 

.1 

< 

sS 

5"« 

s-« 

Jl 

& 

C 

t/5 

(4 

jg 

3 

< 

> 

i 

i 

O 

^ 

jz; 

•< 

H 

u 

> 

f 

• 

Pi 

1 

<£ 

u 

0 

II 

lO  i— i  .— i  1C  i— i  i-H  1C  CO  CO  O  CO ''f 
CTJ     CO  <N  <N  I-H  T-I  O5  CO  *-<  CO  CO  "-I  I-H 


^  (N  CO  (N  *-«  FH        Tj  <N  C<  I-H  <N  CO  (N 


lOOOOOO! 


OCO 


r-KNCO^  >O 


DESIGN  OF  IRRIGATION   STRUCTURES 


53 


(N  iO  O5  CO  iO  t^  00  CO  1C  O 

co  co  O5  "tf1  Tt<  co  o  co  i— i  co 


OCOCOO5OcO(MTfr- ( 


NOCOfe' 

•^  CO  i-H  O  Tt<  CO  IO 

<N  O5  C5  CO  O  O  C<i 

co  co  co  co  co  co  co 


OCOO<NOCOO<NcOCCCi 

»OOCOQOiOOCOGOl>.i— IIO 

TH  C<1  CO        i— I  (M  CO  CO  CO 


<N  IXN  <N  r^  (N 


i-H  (N  CO  TjH  1C  CO  t>- 

CO  CO  CO  CO  CO  CO  CO 


54 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


£| 

CJ 

ft 

1 

E 

$ 

w 

i 

*o 

a 

g 

H 

"-3 

K 

*rt 

& 

| 

1 

i 

ta 

!c  2 

"•         HP* 

H     ^ 

55     en 

W      § 

u 

ail 

£ 

1 

o  — 

tig; 

Id    U   J 

CC 

u 

id    «    ° 

W       "ft-        M 

•SEJJ 

•< 

,4 

& 

a    w 

_ 

«  -s 

C 

0 

8| 

w  i 

% 

3  a 

o 

> 

1 

< 
O 

> 

E 

M 

(2 

Pi 

a 

II 

•§  I 

8cs 

u,.2  u 
S.ti'o 


IT  "  "5  *  * 

| 

O 


o    .  c 

§§•= 


p  x>« 

>"OT3 
g   C   C 


o 

"O  CO  TT' 


1  O  O OOOOOOOO 
1  oo  oo  oo  oo  oo ' 

(N  (N  <M  (N  (M 


!>!>. 

i  00  *O 


00 


g^HTt^iO^OiO^GOt^QO 
QOO5O5O5O5'— "COOO3CO 
i— I^Hi— Ir-li— li-HC^i-^C^i— *C<I 

00000000000 


OiOI>»^QOr^l>t^t^t^COCOCOCOCOCOiOiOiO 

i-Hi— li-HrHOOOOOO'-^'— (T— li— (i-Hi— »OOO 


DESIGN   OF   IRRIGATION   STRUCTURES 


55 


e 
0  o 

^2 
58 

u   en 


CO 
(N 


t^.        t^  O5 

(N        rHi-H 


rt, 
a>" 


o-c 

C3    O 

£8 

6  g 


u.  en 

II 

!l 

£3 
wo 


11 


I— IT— (C^l— I  1— ' Id'— iC^l— I  1— I  1— lT-HdCv:l»-HO3'— I 


i^i^c^^c^c^c^^c^ 


56 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


DESIGN   OF   IRRIGATION   STRUCTURES 


57 


Je 
• 


s. 

o  p 


0) 

'2 
I 


"S 

m 

J3 

w 

rt 

°^ 

rt 

en 

T^ 

-0 

*S 

1 

•°    OJ 

.2  ^ 

1 

1 

g 

^3 

cj 

1* 

H 

B     JS 

bib 

^ 

tn 

rt  u"S 

•    •. 

C/D 

^O 

— 

^^ 

en  D  tu 

1 

*o 
1 

1 

1 

£T 

1 

i 

be 

1 
J 

36S 

F  i-8  1 

**n      T3  b>. 
flj        •     ^>    • 

§^  |?Si 
;;&>  5lgw 
•"3--  .?  J-8 

•g  g^fe  2  i"  c  «» 

If!  j|n 

C  2  hfi-"-"   S   rt  «S 
g-^ffiS  cn^   en 

S  g-g  S  6-S  6 

•ai^ 

.0 

eg  «» 

°§D^ 

iis! 

bfl£  a)  g 

gx-fi 

•^  sp|  g 

ls:sl 

fees-2 

r  bottom;  some  weeds, 
slick,  black  volcanic  ash. 
Drained  sand;  no  weeds. 

§* 

0   ' 

PQ 

,  ^~ 

32* 

ss* 

« 

-v-^— 

o  o 
§§ 

com 

3 
0 

O   O 

o  o 
CQCQ 

15 
£ 

O 

o 
W 

3 

o       ^  >^<      y« 

2  x-g-c  xi 

loslll 

- 
.Uls 


*   .1 

.o'ffi  ^ 


8888888888  ^ 

i— Ii-Hi— Ir-lTHrHi-MT-HrHi—l      O 


CD  COO5i-l 


OOiOOOOfN  <M 


OOiOiOiO 


N-  b-  Tt<  iC^-H  O  O5  (N  CO  O  I-H  I>  CO  IO  CO  ^        t^  T}H        00        O  <N  O5 

^i  CO  C^  iO  ^O  ^O  ^O  ^"^  ^5  '^          t^*  O^  C^  C^l  '"^  <^       oo  ^^        r*^        CO  C^l  t^^ 

TH  O  i— I  i-H  rH  T-H          OO          i-H          i— I  CO  O  i-H  O  O 


OOOOOO        OO       C<l        r-i  CO  O  i— i  O  O 


I-H  CO  00  00  O5  00  »O  T-I  »-H  i—  I  O  C<l  I-H 


i—  I  O  C<l  I-H  CO  O5        OO 

i-H  ^  -^  rH  CQ  t>-          lOrH 


l^c^g^c^^O^        2<Nt-co^      co<N 

I  CO  i— i        i— i  r-i  rJH  CO  CO 


00 
lO 


CO  l>  I-H  CO  <N  (N 
Tt<  (N  i—  i  <N 


I-H  <N  OO 


O  TH  00  O5  O  TH  C^ 

TH  TH  C^  <M  COCOCO 


58 


WORKING   DATA   FOR    IRRIGATION   ENGINEERS 


-  ^ 

H     i-H 

^g  s 

"53    U     ° 

ill 

*d=a 


a| 
?s 


§« 


-      -M 

F 


a 


iiiiiy 
jitUfii 

g^Sl^ocS 

m»§j 


g   tr!  C 

lii 


g.2rs'5 

*•*  "t^    KA  crt 


n   «  ** 

o 


nJ   tnX3   ^   CJ2'O-M 


O  OO  CD  OO  CO  00  ' 
cO  CO  CD  CO  CO  CO  I 


—  icOOi—  ii-HT-HC<liOCvltoC<liOC<>cX)'—  i 


co 


DESIGN   OF   IRRIGATION   STRUCTURES  59 

.020  nor  more  than  .025.  The  canal  is  designed  on  the  basis  of 
mean  velocity  of  2.5  feet  per  second,  and  n  =  .0225,  and  the 
hydraulic  radius  is  4.  If  the  value  of  n  should  actually  be  .020, 
instead  of  .0225,  as  assumed,  what  would  be  the  resulting  velocity? 
Fig.  33  gives  a  handy  means  of  determining  this  (see  explanation 
on  page  82).  We  read  from  this  diagram  that  the  relative  veloci- 

0  51 
ties  for  n  =  .0225  and  .020  are  as     .       and  the  velocity  with 

n  =  0.20  would  therefore  be  2.5  X  ^—  =  2.81.     This  velocity 

U.4o4 

is  higher  than  is  considered  safe,  and  the  designed  velocity  must, 
therefore,  be  reduced  to  2.4  or  less.  In  other  cases  it  is  desirable 
to  know  what  effect  a  change  in  the  value  of  n  may  have  on  the 
slope.  This  may  also  be  ascertained  from  Fig.  33.  A  saving 
of  a  few  feet  in  grade  may  be  the  means  of  reclaiming  many 
additional  acres  of  land,  and  a  reduction  of  the  value  of  n  by 
lining  the  canal  might  bring  this  about.  For  example:  We 
read  from  Fig.  33  that  an  unlined  canal  having  a  hydraulic 
radius  of  5  feet  and  a  value  of  n  of  .025  requires  a  slope  of 

6 

=  2.69  times  as  great  as  the  same  canal  lined  so  as  to  bring 


the  value  of  n  down  to  0.15.  This  problem  is  most  important 
in  the  smaller  canals  which  require  relatively  steep  slopes. 
Other  problems  present  themselves  in  the  solution  of  which  this 
diagram  is  very  useful.  It  is  a  requirement  of  good  design  to 
make  calculations  on  the  basis  of  various  combinations  of  the 
hydraulic  elements  rather  than  on  a  single  set  of  assumptions, 
as  the  latter  may  lead  to  disastrous  results  if  the  assumptions 
should  prove  to  be  erroneous. 

Freeboard.  —  By  freeboard  is  meant  the  vertical  distance  from 
the  maximum  flow  water  surface  to  the  top  of  bank.  The 
requirement  for  a  certain  amount  of  freeboard  is  obvious.  This 
is  not  susceptible  of  mathematical  calculation,  and  its  value 
must  be  based  on  experience  and  accepted  practice.  For  earth 
canals  it  is  seldom  made  less  than  one  foot  for  the  smallest 
canals  (not  considering  small  laterals,  for  which  the  freeboard 
may  be  even  less)  nor  greater  than  three  to  four  feet  for  the 


60  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

largest  canals.  These  figures  are  for  seasoned  banks;  when  the 
banks  are  built,  provision  should  be  made  for  subsequent  settle- 
ment and  wearing  down,  due  to  travel  on  the  banks,  and  in 
certain  localities  for  wind  erosion.  For  well-constructed  banks 
an  allowance  of  about  10  per  cent  should  be  sufficient  for  the 
former,  while  the  latter  is  entirely  dependent  upon  local  condi- 
tions, but  in  most  localities  should  not  be  an  important  item 
with  properly  maintained  canals. 

For  lined  canals  the  freeboard  is  usually  made  relatively 
considerably  less  and  is  dependent  in  some  degree  upon  the 
velocity  of  flow.  For  higher  velocities  the  freeboard  is  generally 
increased  somewhat,  especially  at  points  where  changes  in  grade 
occur,  on  account  of  the  uncertainties  existing  in  the  calculations 
of  depth  of  flow.  Under  high  velocities  the  water  surface  fluc- 
tuates more  and  is  more  disturbed  even  under  theoretically 
uniform  flow,  so  that  it  is  necessary  to  add  a  factor  of  safety 
in  additional  depth  of  freeboard.  In  general,  it  may  be  stated 
that  the  freeboard  for  lined  canals  with  normal  velocities  should 
be  about  one-half  that  required  for  earth  canals  of  correspond- 
ing size. 

Where  a  lined  canal  having  high  velocities  passes  around  a 
sharp  curve  the  water  piles  up  on  the  outside  of  the  curve,  due 
to  its  tendency  to  continue  on  the  tangent.  In  such  cases  it  is 
necessary  to  raise  the  lining  on  the  outside  above  the  normal 
freeboard,  not  only  to  allow  for  the  piling  up  of  the  water  but 
because  of  the  greater  disturbance  of  the  water  at  this  point. 
The  amount  the  water  rises  on  the  outer  side  of  the  curve  may 
be  calculated  approximately,  and  the  value  thus  calculated 
should  be  increased  50  to  100  per  cent  to  allow  for  the  increased 
disturbance  of  the  water  surface.  An  approximate  method  of 
calculating  the  rise  of  water  in  passing  around  curves  is  as 
follows: 

Consider  any  section  made  up  of  three  plane  surfaces,  as  in 
the  figure  on  opposite  page: 

Let  g  =  acceleration  of  gravity  =  32.2  ft.  per  second,  per 

second, 

V  =  velocity  of  water  in  feet  per  second, 
R  =  radius  of  curve  in  feet, 


DESIGN  OF  IRRIGATION   STRUCTURES  61 

F  =  centrifugal  force, 
G  =  force  of  gravity. 

Consider  a  unit  of  mass  and  the  forces  acting  on  it, 

72 
thenF  =  —  =  and  G  =  i. 


Equilibrium  will  be  established  when  there  is  no  tangential 
force  acting  parallel  to  the  surface  A-B,  which  condition  obtains 


when   the   resultant  P,  of  F  and  G,  is  perpendicular  to  A-B. 
We  can  then  write  the  following  equations: 

p  =  G  -v-  cos  9  =  F  -T-  sin  6 
:.  F  =  GtanO  =  tanO 


Since  the  velocity  of  the  water  is  the  same  on  the  curve  as  on 

tangent,  or  only  very  slightly  smaller,  the  area  of  cross-section 

remains  the  same,  and  we  then  equate  the  two  areas  as  follows: 

by  +  fcoia  +   **+**y<»ta    =bd  +  d,cota    _   (2) 

Simultaneous  solution  of  equations  (l)  and  (2)  gives  the  values 
of  x  and  y  as  follows  : 
.         f\  V2b+2yV2cota 

gR-V*cota 
substituting  this  value  of  x  in  equation  (2) 


For  simplicity  let  2  (g  R  -  V  2  cot  a)  =  K, 
then 


2(Kcota+4V2cof*a') 


62  WORKING   DATA   FOR   IRRIGATION   ENGINEERS 

The  depth  of  water  on  outside  of  curve  being  equal  to  x  -f- 
y,  the  height  of  lining  must  be  increased  an  amount  equal  to 
(x  +  y)  —  d  in  order  to  maintain  the  same  freeboard  as  on 
tangents.  To  care  for  the  greater  disturbances  of  water  surface 
on  the  curve,  the  additional  freeboard  should  be  [(x  +  y)  —  d] 
multiplied  by  1.5  to  2. 

For  vertical  sides, 

y  =  d-\x 

V2b 
and  x  =  —  -. 


Chutes.  —  Chutes,  or  inclined  drops,  are  generally  constructed 
of  wood  or  concrete,  the  smaller  structures  as  a  rule  being 
constructed  of  the  former,  while  the  larger  structures  are  con- 
structed of  the  latter.  Open  channels  are  preferable  for  this 
purpose  because  there  is  no  danger  of  their  becoming  clogged 
up,  but  pipes  are  sometimes  used.  The  latter  should  be  pro- 
tected at  the  intake  by  a  suitable  screen. 

The  design  of  an  open  chute  is  a  process  of  successive  approx- 
imation and  is  best  explained  by  means  of  a  concrete  example  : 

•Assume  a  canal  of  500  second-feet  capacity;  the  chute  is  1,000 
feet  long  and  has  a  total  drop  of  20  feet,  giving  a  slope  of  .02. 
The  channel  is  to  be  of  concrete  with  side  slopes  of  1  to  1  ;  the 
probable  value  of  n  is  .013.  There  are  two  cases  to  consider:  one 
of  variable  slope  and  the  other  with  uniform  slope  from  intake 
to  outlet.  The  processes  to  be  followed  in  the  two  cases  are 
similar,  so  that  for  simplicity  of  explanation  the  latter  will  be 
assumed.  (Whether  the  slope  is  to  be  uniform  or  variable  in  a 
particular  case  depends  upon  the  profile  of  the  ground.)  The 
velocity  at  the  lower  end  of  this  steep  channel  will  be  much 
greater  than  at  the  upper  end,  and  therefore  the  cross-section 
must  be  gradually  contracted.  The  variation  in  cross-section 
is  not  uniform,  and  in  order  to  approach  approximately  the 
theoretical  cross-sections  the  total  length  is  divided  into  a 
number  of  short  reaches  and  the  average  cross-section  calculated 
for  each  reach.  The  most  rapid  change  in  velocity  and  cross- 
section  occurs  at  the  beginning  of  the  channel,  and  the  lengths 
of  reaches  are  made  shorter  here  than  is  necessary  further 
downstream,  where  the  transition  is  more  gradual.  The  accom- 


DESIGN   OF   IRRIGATION   STRUCTURES 


63 


panying  table  gives  the  results  of  the  design  of  the  channel  in 
question,  which  was  calculated  with  the  assistance  of  Figs.  6,  16, 
and  34.  The  velocity  at  the  intake  was  assumed  as  2  feet  per 
second.  The  velocity  head  at  the  intake  is,  therefore,  0.06  feet 
and  the  total  head  is  the  same.  The  total  head  at  Sta.  0  +  50 
is  0.06  +  the  drop  of  water  surface  in  50  feet  =  1.06  feet.  The 
design  of  the  cross-section  at  the  intake  consists  merely  in  deter- 
mining bottom  width  and  depth,  which  will  give  the  required 
area,  500  -*-  2  =  250  square  feet.  An  infinite  number  of  dif- 
ferent sections  will  fulfil  this  requirement,  but  the  one  selected  is 
b  =  30  and  d  =  6.8.  Before  designing  the  section  at  Sta.  0  +  50, 
we  note  that  the  total  available  head  is  1.06  feet.  Since  the  av- 
erage velocity  in  this  reach  must  necessarily  be  comparatively 
low,  the  friction  head  will  be  small,  and  therefore  most  of  this 
head  will  be  available  for  accelerating  the  velocity.  Hence,  we 
assume  that  the  probable  velocity  at  Sta.  0  4-  50  is  about  8  feet 
per  second,  which  corresponds  to  a  velocity  head  of  about  1.0 
foot.  By  trying  several  velocities  in  the  neighborhood  of  8  feet 
we  finally  arrive  at  the  quantities  as  shown  in  the  table.  The  fric- 
tion head,  .02,  is  calculated  by  taking  the  velocity  as  the  aver- 
age of  2  and  8.2  or  5.1  and  the  hydraulic  radius  as  the  average 
of  5.08  and  2.32  =  3.7.  The  sum  of  friction  head  and  velocity 
head  must  equal  the  total  head,  which  criterion  establishes  the 
correctness  of  the  section.  Here  also  b  =  18  and  d  =  2.92  is 
not  the  only  combination  which  will  fulfil  the  requirements;  the 
bottom  width  might  be  increased  and  the  depth  decreased,  or 
vice  versa.  The  proper  section  to  choose  is  a  matter  of  judgment 
based  on  considerations  of  economy  and  simplicity  of  construc- 
tion. 


Station 

Total 
Head 

Velocity 
Head 

Friction 
Head 

R 

V 

Bottom 
Width 

Depth 

0 

0.06 

0.06 

0 

5.08 

2.0 

30 

6.8 

0+50 

1.06 

1.04 

0.02 

2.32 

8.2 

18 

2.92 

1  +  00 

2.06 

1.91 

0.15 

1.90 

11.1 

17 

2.32 

2+00 

4.06 

3.36 

0.70 

1.66 

14.7 

15 

2.03 

3  +  00 

6.06 

4.43 

1.63 

1.58 

16.9 

13 

1.96 

4+00 

8.06 

5.2 

2.86 

1.55 

18.3 

12 

1.94 

5+00 

10.06 

5.8 

4.26 

1.53 

19.3 

11 

1.97 

7  +  00 

14.06 

6.5 

7.56 

1.55 

20.5 

10 

2.02 

10+00 

20.06 

7.1 

12.96 

1.50 

21.4 

10 

1.95 

64  WORKING   DATA  FOR   IRRIGATION   ENGINEERS 

By  a  similar  process  each  successive  cross-section  is  designed, 
successive  approximations  of  the  velocities  being  made  each 
time,  and  the  friction  head  calculated  from  the  average  hydraulic 
radius  and  velocity  between  stations.  This  example  was  selected 
at  random  and  is  given  as  an  illustration  of  the  process  only.  It 
is  not  intended  to  represent  a  good  design,  although  it  might  be 
considered  satisfactory.  Local  conditions  exercise  an  important 
influence  on  the  choice  of  cross-sections,  but  whatever  sections 
are  decided  upon,  they  must  fulfil  the  hydraulic  requirements 
as  illustrated  in  the  table.  Great  refinements  are  not  necessary 
nor  justified.  As  an  illustration:  If  the  bottom  widths  and 
depth  shown  in  the  table  were  satisfactory,  it  would  be  good 
engineering  to  make  the  first  three  depths  6.8,  2.9,  and  2.3 
respectively,  and  the  remaining  ones  an  even  2  feet. 

A  point  sometimes  lost  sight  of  in  designs  of  this  kind  is  that 
it  is  the  slope  of  the  water  surface  and  not  the  grade  of  the  bottom 
of  the  channel  that  determines  the  velocity. 

Sudden  reductions  in  rate  of  grade  should  be  avoided  if 
possible,  on  account  of  the  disturbances  of  the  water  surface 
that  occur  at  such  points.  If  sharp  reductions  of  grade  are  un- 
avoidable, the  freeboard  should  be  increased  above  the  normal 
to  provide  for  the  disturbed  conditions.  In  the  case  of  pipe 
chutes,  the  conditions  are  reversed  and  sharp  increases  in  grade 
should  be  avoided,  and  if  possible  the  profile  of  the  pipe  should 
be  kept  concave  upward.  This  is  desirable  on  account  of  the 
tendency  toward  the  formation  of  a  vacuum  at  points  where 
a  sudden  increase  in  grade  occurs,  and  this  tendency  is  most 
pronounced  when  the  pipe  is  running  on,  or  just  below,  the 
hydraulic  gradient. 

Flumes. — The  design  of  flumes  does  not  offer  any  special 
hydraulic  problems.  They  are  generally  designed,  and  properly 
so,  for  a  higher  velocity  than  exists  in  the  canal  above,  and  it 
must  be  remembered  that  head  to  produce  the  increased  velocity 
must  be  provided  at  the  intake.  For  example,  if  the  velocity  in 
the  canal  is  2.5  feet  per  second,  and  that  in  the  flume  6  feet  per 
second,  the  extra  drop  to  be  provided  at  the  head  of  the  flume  is 

62  —  2.52 
— - — '• — =  0.461  foot.     If  the  entrance  is  sharp  an  additional 

o 


DESIGN   OF   IRRIGATION   STRUCTURES  65 

allowance  must  be  made  for  entry  head.  For  a  square  entrance, 
that  is,  with  headwalls  of  the  intake  perpendicular  to  the  direc- 
tion of  flow,  the  entry  head  is  generally  taken  as  0.5  of  the 
velocity  head,  while  for  a  gradual  transition  the  loss  may  be  as 
low  as  .05  of  the  velocity  head.  The  velocity  head  in  this  case 
is  that  due  to  a  6-foot  velocity,  or  .558  feet,  and  not  the  difference 
in  velocity  heads  calculated  above.  If  the  above  flume  had  a 
square  intake,  the  total  drop  to  be  provided  at  the  intake  would 

then  be  .461  +  ~  =  .74  ft.      At  the  outlet  of  the  flume  a 
2i 

certain  portion  of  the  velocity  head  is  recovered.  The  amount 
of  this  depends  upon  the  construction  of  the  outlet,  and  is  difficult 
to  estimate.  The  more  gradual  the  transition  the  more  head 
will  be  regained.  It  should  not  generally  be  estimated  as  more 
than  0.25  to  0.5  of  the  velocity  head.  The  latter  figure  in  the 
above  case  would  give  0.461  -5-  2  =  0.23  feet  on  the  assumption 
that  the  velocity  in  the  canal  below  the  flume  is  2.5  feet  per 
second. 

For  a  rectangular  flume,  the  greatest  velocity  for  a  given  area 
obtains  when  the  bottom  width  is  twice  the  depth,  as  this  pro- 
portion gives  maximum  hydraulic  radius.  For  a  circular  cross- 
section,  the  maximum  hydraulic  radius  obtains  when  the  depth 
of  water  is  about  1.6  times  the  radius,  and  is  equal  to  about  0.61  R. 
The  hydraulic  radius  is  the  same  for  a  full  circle  as  for  a  semi- 
circle, being  in  each  case  equal  to  0.5  times  the  radius. 

The  hydraulic  elements  of  rectangular  flumes  are  given  in 
Fig.  14.  For  determining  the  discharge  of  small  wood  flumes, 
such  as  are  generally  used  for  irrigation  laterals,  Figs.  23  and  24 
are  very  convenient.  Fig.  29,  in  conjunction  with  Tables  23 
and  24,  gives  the  discharge  of  steel  flumes  of  the  standard  sizes 
now  manufactured.  The  value  of  Kutter's  "  n  "  for  flumes  is 
discussed  under  "  Canals." 

Pipe  Lines. — In  irrigation  work,  wood  and  concrete  are  the 
materials  most  frequently  used  for  pipes,  but  steel  is  used  for 
very  high  heads.  Cast  and  wrought  iron  are  seldom  used  on 
account  of  their  high  cost.  Reinforced  concrete  pipes  up  to  46 
inches  in  diameter  have  been  built  under  heads  as  high  as  110 
feet,  and  it  is  probably  not  safe  to  use  this  type  of  construction, 


66  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

in  consideration  of  our  present  knowledge  of  the  subject,  for 
heads  much  greater  than  this.  Wood  pipes  are  ordinarily  used 
for  heads  up  to  200  feet,  but  may  be  used  up  to  400  feet.  Steel 
pipes  are  specially  adaptable  for  large  pipes  under  heads  greater 
than  200  feet.  Occasionally  two  or  more  kinds  of  material  are 
ased  in  a  single  line. 

The  flow  of  water  in  pipes  has  been  the  subject  of  many 
researches.  Most  of  these  have  dealt  with  cast-iron  pipe,  and  the 
probable  flow  in  these  is  better  established  than  in  pipes  of  any 
other  material.  Wood-stave  pipes  probably  come  next  in  order 
in  the  reliability  of  the  calculations  of  carrying  capacity,  which 
is  somewhat  greater  than  that  of  cast-iron  pipe.  A  considerable 
number  of  observations  have  been  made  on  riveted  steel  pipe, 
but  under  such  widely  different  conditions  that  it  has  been 
difficult  to  coordinate  them.  They  indicate  in  a  general  way 
that  the  carrying  capacity  is  about  10  per  cent  smaller  than  for 
cast-iron  pipe.  Very  few  experiments  have  been  made  on  the 
carrying  capacity  of  concrete  pipe,  and  we  are  forced  to  resort 
to  a  comparison  of  the  interior  surfaces  with  those  of  cast-iron 
and  wood  pipe  to  arrive  at  an  idea  of  its  probable  carrying  capac- 
ity. Concrete  pipe  is  built  in  various  forms  and  by  different 
methods.  There  is  the  dry-mix  pipe,  built  in  short  (usually 
two-foot)  sections,  and  laid  and  jointed  in  a  similar  manner  to 
clay  sewer  pipe,  and  the  wet-mix  pipe,  either  built  and  laid  in 
short  sections  as  aforementioned,  or  built  continuously  in  the 
trench.  In  the  former  case  there  is  more  or  less  roughness  at 
the  joints  with  possible  jogs  in  the  alignment,  while  in  the 
latter  the  continuity  is  unbroken  and  better  alignment  may  be 
obtained.  The  discharging  ability  of  the  continuous  pipe  with 
first-class  workmanship  may  be  as  high  as  that  of  wood-stave 
pipe,  while  the  wet-mix  jointed  pipe  may  better  be  classed  with 
cast-iron  pipes.  However,  in  consideration  of  our  meagre 
knowledge  of  the  subject,  the  use  of  the  cast-iron  pipe  formula 
is  recommended  for  calculating  the  discharge  of  concrete  pipe 
built  continuously  with  steel  forms,  with  a  reduction  of  5  to  10 
per  cent  for  jointed  pipes,  depending  upon  the  amount  of  care 
used  in  producing  a  smooth  interior  surface.  Dry-mix  concrete 
pipe  is  adaptable  only  to  very  low  heads  and  small  diameters 


DESIGN  OF  IRRIGATION   STRUCTURES  67 

on  account  of  the  impracticability  of  reinforcing  it  with  steel. 
It  has  a  considerably  rougher  surface  than  the  wet-mix,  and  its 
carrying  capacity  under  favorable  circumstances  is  probably  not 
greater  than  that  of  riveted  steel  pipe,  and  may  be  considerably 
less,  if  not  very  carefully  laid. 

Many  formulas  have  been  proposed  for  the  flow  of  water  in 
pipes,  and  it  is  difficult  to  decide  which  of  these  to  use.  Experi- 
ments seem  to  indicate  that  we  cannot  hope  to  get  nearer  than 
5  to  10  per  cent  to  the  true  values  from  any  formula,  and  great 
refinements  in  the  calculations  of  size  of  pipe  are,  therefore,  not 
warranted.  The  United  States  Reclamation  Service  has  adopted 
the  following  formulas  *  for  calculating  the  carrying  capacity  of 
pipes : 

Wood-stave  pipe  Q  =  1.35  D  2'7  H  555 

Cast-iron  pipe  Q  =  1.31  D 2'7  H  555 

Concrete  pipe  Q  =  1.24  D  2'7  H  555 

Riveted  steel  Q  =  1.18  D 2'7  H  555 

Q  =  Discharge  in  cubic  feet  per  second. 

D  =  Diameter  of  pipe  in  feet. 

H  =  Friction  loss  in  feet  per  1,000  feet  of  pipe. 

These  formulas  were  derived  from  experiments  on  pipes  of 
four  inches  and  larger  in  diameter,  and  are,  therefore,  principally 
applicable  for  pipes  of  such  sizes.  Pipes  smaller  than  4  inches  in 
diameter  are  seldom  used  for  irrigation  purposes.  Farming's 
formula  is  said  to  give  accurate  results  for  smaller  pipes.  The 
discharges  of  pipes  6  inches  and  smaller  in  diameter,  calculated 
from  Fanning's  formula,  are  given  in  Table  19. 

All  of  the  above  formulas  cover  friction  losses  only.  Addi- 
tional head  must  be  allowed  for  bends,  valves,  etc.  Allowance 
must  be  made  at  the  intake  for  velocity  and  entry  heads.  The 
latter  may  be  taken  as  0.5  times  the  velocity  head  for  a  square 
intake,  0.25  for  a  rounded  intake,  and  0.05  for  a  bell  mouth. 
Practically  no  data  are  available  in  regard  to  the  loss  of  head 
in  curves  in  large  pipes.  There  can  be  no  question  but  that  the 
loss  of  head  is  greater  on  curves  than  on  tangents,  but  as  the 

*See  Engineering  Record,  vol.  68,  p.  667,  for  a  discussion  of  these  formulas  and  a  comparison 
of  17  different  formulas  for  flow  of  water  in  pipes. 


68 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


formulas  are  based  on  experiments  which  included  the  losses  in 
curves  in  "  friction "  losses,  ordinary  curvature  is  probably 
safely  provided  for,  and  separate  calculations  for  the  curve  losses 
are  not  necessary  except  when  the  alignment  and  profile  are 
exceptionally  crooked.  No  experimental  data  are  available  on 
the  losses  in  long,  sweeping  curves,  such  as  occur  on  irrigation 
and  power  lines. 

TABLE   19 

FLOW  OF  WATER,  IN  SECOND-FEET,  IN  SMOOTH,  STRAIGHT  IRON  PIPES,  FOR 
VARIOUS  FRICTION  HEADS,  BASED  ON  FANNING'S  CO- 
EFFICIENTS FOR  FRICTION 

Friction  head,  Hf=4f  ^  or  Q  =  0. 1  Dz  ^-^f- 

l  =  total  length  of  pipe. 
H  =  friction  head  in  length  /. 
H  —  friction  head  per  1,000  feet  of  pipe. 
D  =  diameter  in  feet. 


Inside 
Diameter, 
in  Inches 

Friction  Head,  in  Feet  per  1,000  Feet  of  Pipe 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

0.0019 
.0055 
.0124 
.0221 
.0357 
.0533 
.0752 
.134 
.214 

0.0027 
.0079 
.0178 
.0317 
.0511 
.0765 
.108 
.191 
.306 

0.0034 
.0099 
.0220 
.0392 
.0631 
.0942 
.133 
.236 
.378 

0.0040 
.0116 
.0256 
.0456 
.0734 
.110 
.154 
.275 
.440 

0.0045 
.0131 
.0288 
.0513 
.0824 
.123 
.174 
.310 
.495 

0.0050 
.0145 
.0318 
.0567 
.0907 
.136 
.191 
.340 
.544 

0.0054 
.0158 
.0345 
.0612 
.0986 
.147 
.207 
.368 
.591 

0.0058 
.0170 
.0370 
.0658 
.106 
.158 
.222 
.396 
.634 

0.0062 
.0181 
.0394 
.0701 
.112 
.168 
.237 
.420 
.675 

2 

2|.:  

3  

3§.. 

4    . 

5  

6 

10 

20 

30 

40 

50 

60 

70 

80 

90 

1.  . 

0.0066 
.0192 
.0417 
.0740 
.119 
.178 
.250 
.444 
.713 

0.0098 
.0281 
.0605 
.107 
.171 
.256 
.360 
.639 
1.02 

0.0124 
.0352 
.0749 
.132 
.212 
.316 
.446 
.792 
1.27 

0.0145 
.0414 
.0872 
.154 
.247 
.369 
.520 
.924 
1.48 

0.0165 
.0466 
.0982 
.173 
.278 
.414 
.585 
1.04 
1.67 

0.0183 
.0513 
.108 
.191 
.306 
.456 
.643 
1.14 
1.83 

0.0198 
.0557 
.117 
.207 
.333 
.496 
.698 
1.24 
1.99 

0.0213 
.0598 
.126 
.223 
.357 
.532 
.749 
1.33 
2.13 

0.0227 
.0637 
.134 
.238 
.381 
.566 
.797 
1.42 
2.27 

li  • 

2 

2i. 

3  

si.. 

4 

5 

6 

COEFFICIENTS  OF  FRICTION,/,  FOR  NEW  PIPES  IN  FANNING'S  FORMULA 


Velocity  in  Feet  per  Second 

Diameter 

1 

3 

6 

10 

0.25ft. 

.0071 

.0067 

.0064 

.0062 

0.50ft. 

.007 

.0063 

.006 

.0057 

DESIGN  OF  IRRIGATION   STRUCTURES  69 

Figures  30,  31,  and  32  show  a  plotting  of  the  above  formulas 
from  which  all  the  factors  involved  can  be  looked  out  at  a  glance. 
No  separate  diagram  is  given  for  concrete  pipe,  but  the  cast-iron 
or  riveted  steel  pipe  diagram,  or  an  average  of  the  two,  may  be 
used  for  this  purpose,  depending  upon  the  type  of  construction 
to  be  used  and  the  amount  of  attention  to  be  given  to  producing 
a  smooth  interior  surface. 

The  above  formulas  are  for  new  pipes.  It  is  generally 
assumed  that  wood  pipe  increases  in  carrying  capacity  with  con- 
tinued use,  but  no  reliance  should  be  placed  on  this.  It  may, 
however,  be  safely  assumed  that  a  well-designed  wood  pipe  will 
not  decrease  in  carrying  capacity  with  continued  use.  The  effect 
of  age  on  concrete  pipe  is  not  known,  but  it  is  customary  to 
assume  that  the  carrying  capacity  does  not  decrease,  as  there 
is  no  reason  to  suppose  that  it  should.  Cast-iron  and  steel  pipes 
show  a  marked  decrease  in  carrying  capacity  with  continued  use, 
and  it  is  necessary  that  allowance  be  made  for  this.  Williams 
and  Hazen  assume  that  the  friction  head  increases  3  per  cent  per 
year,  due  to  tuberculation,  and  that  the  diameter  decreases 
0.01  inch  per  year  from  the  same  cause.  Applying  these  factors 
to  the  equation  Q  =  1.31  D  2'7,  H  °'555,  and  letting  K  equal  the 
ratio  of  discharge  at  the  age  of  N  years  to  discharge  new,  we  get 

2.7         i-  -i  0.555 

2000 

Thus  from  this  equation  we  calculate  that  a  12-inch  cast-iron 
pipe  10  years  old  will  carry  85  per  cent  as  much  as  the  same 
pipe  new,  and  at  the  age  of  100  years  it  will  carry  only  36  per 
cent. 

One  of  the  most  important  features  in  the  design  of  pipes 
to  operate  under  pressure  is  to  make  provision  for  preventing 
the  carriage  of  air  through  or  accumulation  of  air  in  the  pipe, 
as  the  presence  of  air  in  a  pipe  decreases  the  capacity  in  a  marked 
degree.  It  is  practically  impossible  to  prevent  the  entrance  of 
air  at  the  intake,  and  for  this  reason  it  is  always  desirable  to 
insert  an  air-relief  pipe  in  the  top  of  the  pipe  a  short  distance, 
say  15  or  20  feet,  below  the  intake  wall.  The  top  of  the  relief 
pipe  should,  of  course,  be  above  the  hydraulic  gradient.  Its 


70  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

size  depends  upon  the  design  of  the  intake,  velocity  of  water, 
etc.,  but  an  area  of  one- twentieth  that  of  the  pressure  pipe  will 
generally  suffice.  In  case  of  doubt  the  air  relief  should  be  made 
larger,  as  this  can  do  no  harm,  or  two  pipes  may  be  used,  located 
from  5  to  10  feet  apart. 

Vertical  Drops. — Drops  are  built  in  canals  for  the  purpose  of 
destroying  excess  grade,  and  their  openings  must  be  of  such  size 
that  the  maximum  discharge  of  the  canal  will  pass  over  them 
without  raising  the  water  upstream  above  the  normal  maximum 
elevation.  The  depth  of  water  on  the  crest  must,  therefore,  be 
calculated  as  for  weirs  and  dams.  Two  types  of  drops  are  used, 
namely,  those  with  rectangular  openings,  and  the  so-called 
"  notched  drops,"  which  have  the  sides  inclined  so  as  to  make 
the  opening  at  the  top  wider  than  at  the  crest.  The  idea  of  the 
latter  is  to  avoid  a  drop-down  surface  curve  when  less  than  the 
maximum  discharge  is  flowing  in  the  canal,  which  in  the  rectan- 
gular form  must  be  accomplished  by  means  of  stop  planks  or 
other  form  of  movable  crest. 

Below  the  weir  of  a  drop  a  water  cushion  or  depression  below 
the  bottom  of  the  canal  downstream  is  usually  built.  The  pur- 
pose of  this  is  to  absorb  the  energy  of  the  fall  and  to  protect  the 
floor  from  impact  of  the  falling  water.  The  proper  depth  of 
water  cushion  is  a  question  to  be  determined  by  experience, 
which  seems  to  indicate  that  a  depth  of  one-third  to  one-half  the 
height  of  fall  is  sufficient.  For  example :  For  a  vertical  drop  of 
6  feet  between  water  surfaces  above  and  below  the  weir,  the 
floor  below  the  weir  should  be  depressed  from  2  to  3  feet  below 
the  normal  bottom  of  canal  for  a  distance  of  two  to  four  times 
the  depth  of  water  in  the  canal,  the  latter  distance  depending 
mainly  on  the  quantity  of  flow.  These  figures  are  merely  sug- 
gestions and  must  be  used  with  discretion.  It  is  impossible  to 
absorb  all  the  energy  of  the  water  in  this  chamber,  and  the  canal 
below  must  be  protected  for  some  distance  downstream  by  means 
of  paving  or  some  form  of  riprap.  The  amount  of  such  protec- 
tion cannot  be  ascertained  in  advance,  and,  moreover,  this  is  not 
essential,  as  additional  protection  can  be  provided  if  necessary, 
after  the  canal  is  in  operation. 

Notched  drops  have  been  used  in  India  to  a  considerable 


DESIGN   OF   IRRIGATION   STRUCTURES  71 

extent,  but  have  been  used  very  little  in  the  United  States.  The 
latter  is  probably  due  to  the  fact  that  coefficients  of  discharge 
for  such  openings  are  practically  unknown,  and  because  it  is 
generally  desirable  on  our  canals  to  use  the  drop  structure  as  a 
check  as  well,  and  for  this  purpose  it  must  be  adjustable.  In 
this  case  there  is  nothing  gained  by  using  a  notched  drop,  and 
rectangular  openings  with  stop-plank  control  are,  therefore, 
preferred. 

Turnouts. — By  a  turnout  is  meant  a  structure  for  diverting 
water  from  a  larger  canal  into  a  smaller.  Turnouts  for  divert- 
ing large  quantities  are  sometimes  open  sluices,  but  the  great 
majority  consist  of  a  closed  tube  controlled  by  gates  on  the  canal 
side.  These  tubes  are  nearly  always  so  short  that  friction  in  the 
tube  may  be  neglected,  and  provision  need  only  be  made  for 
velocity  and  entry  heads.  The  tube  should  be  set  low  enough 
in  the  bank  so  that  it  can  extract  the  required  quantity  of  water 
with  the  minimum  head  in  the  main  canal  at  which  the  turnout 
is  to  be  operated.  A  general  rule  in  a  new  system  is  to  set  the 
turnout  tube  so  that  it  can  extract  its  maximum  required  dis- 
charge when  the  canal  from  which  it  diverts  is  running  at  one- 
half  to  two-thirds  of  its  maximum  depth.  For  tubes  built  flush 
with  the  face  of  the  headwall  of  the  turnout,  an  allowance  for 
entry  head  of  0.5  the  velocity  head  is  generally  made.  Turnouts 
are  ordinarily  designed  for  velocities  of  3  to  5  feet  per  second. 
Comparatively  low  velocities  are  necessary,  as  a  measuring 
device  is  usually  placed  just  below  the  outlet  of  the  tube  and 
high  velocities  would  vitiate  the  accuracy  of  measurements. 
Turnouts  should  not  be  operated  under  pressure  on  account  of 
the  danger  to  the  bank  in  case  leaks  should  develop.  For  this 
reason  the  location  of  regulating  gates  at  or  near  the  outlet  of 
the  tube  is  very  ill  advised. 

Culverts. — Where  canals  cross  drainage  channels  it  is  neces- 
sary to  provide  culverts  for  carrying  the  cross-drainage  under 
the  canal.  These  do  not  differ  materially  from  culverts  under 
highways  and  railroad  grades,  except  that  greater  care  must  be 
exercised  in  their  location  and  construction.  They  must  be 
provided  with  cut-off  walls  on  either  side  of  the  water  section 
of  the  canal,  and  if  possible  the  top  of  the  culvert  should  be  at 


72  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

least  two  feet  below  the  bottom  of  the  canal  to  prevent  excessive 
seepage  of  water  from  the  canal  along  the  outside  of  the  culvert. 

The  principal  hydraulic  problem  in  connection  with  the 
design  of  culverts  is  the  determination  of  the  probable  maxi- 
mum discharge  of  the  drainage  channel.  This  is  a  vexatious 
problem  at  best,  but  it  is  most  difficult  in  arid  regions,  where  it 
is  not  uncommon  for  a  channel  to  remain  absolutely  dry  for  a 
number  of  years,  and  then  suddenly,  due  usually  to  a  cloudburst, 
discharge  many  hundred  second-feet.  It  is  not  advisable  here, 
as  in  railroad  culverts,  to  build  first  a  temporary  structure  and 
replace  this  later  by  permanent  construction  after  better  data 
have  accumulated  in  regard  to  the  run-off,  as  the  bed  and  banks 
should  not  be  disturbed  after  they  have  once  become  seasoned, 
and  wooden  structures  under  large  canals  are  dangerous.  It  is, 
therefore,  necessary  to  make  the  construction  permanent,  and 
the  opening  must  be  built  sufficiently  large  to  carry  the  largest 
possible  flood.  The  best  method  of  determining  the  most  prob- 
able maximum  flood,  in  the  absence  of  actual  gagings,  is  to  make 
measurements  of  the  slope  and  cross-sections  of  the  channel  at 
high-water  marks  and  calculate  the  discharge  by  means  of 
Kutter's  formula.  High-water  marks  can  usually  be  found  at 
points  where  the  channel  is  well  defined.  The  value  of  n  to 
be  used  in  the  calculations  depends  upon  the  nature  of  the 
channel.  After  calculating  the  discharge  at  various  points,  the 
maximum  value  found  should  be  multiplied  by  2  or  3,  depend- 
ing upon  the  probable  reliability  of  the  data.  This  is  on  the 
assumption  that  no  measurements  are  available  of  the  actual  flow. 
Formulas  based  on  the  area  of  watershed  are  practically  useless 
in  arid  regions,  although  cases  occur  where  the  use  of  such  a 
formula  offers  the  only  available  solution. 

After  the  maximum  discharge  has  been  estimated,  the 
opening  is  designed  in  a  similar  manner  to  turnout  tubes. 
The  openings  are  generally  designed  for  a  velocity  of  about  10 
feet  per  second.  Much  higher  velocities  are  not  advisable  on 
account  of  excessive  eddying  at  the  intake  and  washing  of  the 
channel  below  the  outlet.  The  use  of  lower  velocities  may  be 
necessary  on  account  of  lack  of  sufficient  head,  but  this  is  un- 
usual. 


HYDRAULIC   DIAGRAMS 
AND  TABLES 


CHAPTER  IV 

HYDRAULIC   DIAGRAMS  AND  TABLES 

Figs.  4  to  13  inclusive  give  slopes  and  velocities  for  varying 

values  of  hydraulic  radius  and  for  values  of  n  from  .010  to  .035, 

the  common  range  of  practice.    Kutter's  formula  is  the  basis  of 

these  diagrams,  and  the  following  suggestions  are  offered  as  an 

aid  in  the  selection  of  the  proper  value  of  n: 

n  =  .010  for  straight  and  regular  channels  lined  with  matched 
planed  boards;  neat  cement  plaster;  or  glazed,  coated,  and 
enameled  surfaces  in  perfect  order.  This  value  is  seldom 
used  in  practice. 

n  =  .012  for  straight  and  regular  channels  lined  with  unplaned 
timber  carefully  laid;  sand  and  cement  plaster;  or  best  and 
cleanest  brickwork. 

n  =  .013  for  straight,  regular  channels,  lined  with  concrete, 
having  a  steel  trowelled  surface  in  good  order. 

n  =  .014  for  straight,  regular  channels  lined  with  concrete,  hav- 
ing a  wooden  trowelled  surface  in  good  order. 

n  =  .015  for  straight  and  regular  channels  of  ordinary  brickwork; 
smooth  stonework;  or  foul  and  slightly  tuberculated  iron. 

n  =  .020  for  channels  of  fine  gravel;  rough  set  rubble;  ruined 
masonry;  or  tuberculated  iron;  or  for  canals  in  earth,  in  good 
condition,  lined  with  well-packed  gravel,  partly  covered  with 
sediment,  and  free  from  vegetation. 

n  =  .0225  for  canals  in  earth  in  fair  condition  lined  with  sediment 
and  occasional  patches  of  algae,  or  composed  of  firm  gravel 
without  vegetation. 

n  =  .025  for  canals  and  rivers  of  tolerably  uniform  cross-section, 
slope  and  alignment  in  average  condition,  the  water  slopes 
being  lined  with  sediment  and  minute  algae,  or  composed  of 
loose,  coarse  gravel;  also  for  very  smooth  rock  sections. 

n  =  .030  for  canals  and  rivers  in  rather  poor  condition,  having 
the  bed  partially  covered  with  debris,  or  having  compara- 

75 


76  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

tively  smooth  sides  and  bed,  but  the  channel  partially  ob- 
structed with  grass,  weeds,  or  aquatic  plants;  also  for  aver- 
age rock  sections. 

n  =  .035  for  canals  and  rivers  in  bad  order  and  regimen,  having 
the  channel  strewn  with  stones  and  detritus,  or  about  one- 
third  full  of  vegetation;  also  for  rough  rock  sections. 
Canals  in  earth  with  their  channels  half  full  of  vegetation  may 
have  n  =  .040,  and  when  two-thirds  full  of  vegetation  may  have 
n  =  .050.     In  exceptional  cases  the  value  of  n  may  reach  .060. 
It  will  be  noted   that  the  velocities  in   Figs.  4  to  8  for 
values  of  n  up  to  .015  range  from  2  to  35  feet  per  second.    Chan- 
nels in  which  these  values  of  n  are  applicable  are  usually  of  such 
construction  that  velocities  less  than  2  feet  are  seldom  used,  and 
velocities  over  35  feet  per  second  are  uncommon  in  any  case. 
These  limits  have,  therefore,  been  adopted  in  order  to  get  as 
large  a  scale  as  possible.    Similarly,  in  Figs.  9  to  13  inclusive,  for 
values  of  n  .020  to  .035,  the  range  of  velocities  is  from  1  to  20 
feet  per  second.    These  values  of  n  apply  especially  to  unlined 
channels  in  which  velocities  greater  than  20  feet  and  less  than 
1  foot  per  second  are  very  uncommon. 

The  scales  of  coordinates  are  all  logarithmic,  that  is,  instead 
of  the  actual  distances  or  values  measured  in  linear  units  being 
laid  off  on  the  vertical  and  horizontal  axes,  the  logarithms  of 
these  values  are  laid  off,  just  as  is  done  on  the  ordinary  slide  rule. 
In  fact,  in  the  preparation  of  several  of  the  diagrams  in  this 
book  the  scales  were  transferred  directly  from  a  20-inch  slide 
rule.  Interpolations  are  made  exactly  as  in  linear  scales,  as  the 
lines  have  been  made  sufficiently  close  together  so  that  linear 
interpolation  is  sufficiently  exact.  The  great  advantage  in  the 
use  of  logarithmic  scales  is  that  a  large  range  of  values  can  be 
covered  with  the  same  degree  of  accuracy  throughout,  which  is 
impossible  on  linear  scales.  As  an  illustration  of  the  difference 
between  the  logarithmic  and  linear  scales,  refer  to  Fig.  4,  and 
suppose  that  the  values  of  R  were  plotted  throughout  on  the 
same  scale  as  that  used  from  R  =  .2  to  R  =  .3.  The  distance 
between  the  two  is  about  one-half  inch,  that  is,  each  half -inch 
represents  a  range  of  0.1  in  the  value  of  R.  If  this  scale  were 
continued  up  to  R  =  10,  we  would  have  a  diagram  49  inches  high 


HYDRAULIC  DIAGRAMS  AND  TABLES  77 

instead  of  only  5  inches.  A  similar  increase  would  occur  in  the 
horizontal  scale  if  linear  values  of  V  were  plotted.  The  linear 
scales  would,  of  course,  allow  a  more  exact  reading  of  the  dia- 
gram for  the  higher  values,  but  this  is  not  necessary,  nor  even 
desirable,  as  the  logarithmic  diagram  gives  as  high  a  degree  of 
accuracy  as  is  warranted  by  the  formula  and  the  data  upon  which 
its  use  is  based.  A  further  advantage  of  the  logarithmic  plotting 
is  that  the  curves  are  straightened  out  and  consequently  easier 
to  read. 

The  manner  of  using  the  diagrams,  Figs.  4  to  13,  is  evident. 
Given  any  two  of  the  three  variables,  the  third  is  looked  out  from 
the  diagram  either  directly  or  by  ocular  interpolation  without  any 
calculations.  For  the  convenience  of  those  who  wish  to  know 
or  make  use  of  the  value  of  c  in  the  formula  V  =  CV  R  S,  these 
are  given  for  the  corresponding  value  of  n.  Table  21  gives  a 
summary  of  these  tables  for  all  values  of  n. 

Figs.  14  to  20  give  the  hydraulic  elements  of  rectangular  and 
trapezoidal  channels.  Each  of  these  diagrams  may  be  consid- 
ered as  being  made  up  of  two  separate  diagrams,  the  upper 
portion  giving  the  relation  between  area,  velocity,  and  discharge, 
and  the  lower  giving  the  relation  between  the  depth,  area,  bottom 
width,  and  hydraulic  radius.  All  scales  are  logarithmic.  The 
horizontal  scale  is  identical  for  upper  and  lower  portion,  and 
forms  the  medium  through  which  the  two  parts  are  connected. 
The  manner  of  constructing  the  diagrams  must  be  obvious, 
except,  perhaps,  the  manner  of  plotting  the  hydraulic  radius 
curves.  These  were  plotted  after  the  bottom  widths  had  been 
plotted;  the  points  were  located  on  the  bottom  width  lines  by 
calculating  the  depths  which,  for  the  given  bottom  width,  would 
give  the  required  hydraulic  radius;  the  locus  of  one  set  of  such 
points  forms  a  hydraulic  radius  curve. 

To  avoid  an  excessively  large  page  and  folded  sheets,  three 
pages  are  used  for  each  type  of  channel.  Each  page,  however, 
is  a  complete  diagram  for  the  range  of  values  that  it  covers. 
The  first  page  of  each  set  is  used  for  small  channels,  the  second 
for  medium-sized  channels,  and  the  third  for  large  channels.  For 
Figs.  19  and  20,  only  one  page,  that  for  large  channels,  is  used, 
as  tjiere  is  seldom  occasion  to  use  mixed  slopes  on  canals  of 


78  WORKING  DATA  FOR   IRRIGATION   ENGINEERS 

smaller  size  than  those  covered  by  this  diagram.  It  should  be 
noted  that  Fig.  19,  which  was  computed  on  the  basis  of  one 
side  slope,  1J  to  1,  and  the  other  1  to  1,  is  applicable  also  to 
channels  having  both  side  slopes  1J  to  1,  the  areas  being  exactly 
the  same  and  the  hydraulic  radii  only  very  slightly  different. 
Similarly,  Fig.  20  is  applicable  to  channels  having  both  side 
slopes  if  to  1. 

In  the  upper  portion  of  the  diagrams,  velocities  up  to  10  feet 
per  second  are  covered,  but  velocities  higher  than  this  are  fre- 
quently used;  also,  the  entire  width  of  the  diagram,  that  is,  the 
entire  range  of  areas  is  covered  by  only  one  velocity,  namely, 
2  feet  per  second.  The  diagram  is,  however,  arranged  so  that 
by  mentally  moving  the  decimal  point  any  velocity  can  be  used. 
As  an  illustration  of  this,  refer  to  Fig.  15,  Part  2,  and  assume  that 
a  channel  has  a  bottom  width  of  18  feet,  a  depth  of  4  feet,  and  a 
velocity  of  5  feet  per  second.  What  is  the  discharge?  In  the 
lower  part  of  the  diagram,  we  find  the  intersection  of  the  line 
representing  a  depth  of  4  with  the  line  representing  a  bottom 
width  of  18;  thence  vertically  to  the  line  in  the  upper  portion  of 
the  diagram  representing  a  velocity  of  0.5  (not  5)  feet  per 
second,  and  read  the  discharge  40  c.  f.  s.  Now,  since  the  velocity 
is  10  times  that  used  in  finding  this  quantity,  the  actual  discharge 
is  400  c.  f .  s.  instead  of  40.  This  illustration  represents  a  very 
simple  case,  but  further  inspection  will  show  that  the  diagram 
can  be  used  for  any  velocity  by  properly  manipulating  the  deci- 
mal point.  Further  examples  are  worked  out  on  the  pages  oppo- 
site the  diagrams. 

Fig.  21,  consisting  of  two  sheets,  gives  the  hydraulic  elements 
of  circular  segments  for  radii  of  0.5  foot  to  8  feet.  The  horizontal 
scale  represents  the  depths  of  water  and  the  vertical  scale  the 
corresponding  areas.  The  hydraulic  radii  are  shown  in  the  same 
manner  as  for  rectangular  and  trapezoidal  channels  in  Figs.  14 
to  20.  For  values  of  the  radius  R  not  covered  in  the  diagram 
either  directly  or  by  interpolation,  the  table  on  page  146  opposite 
the  diagram  may  be  used. 

Fig.  22  gives  the  discharge  and  velocity  of  circular  conduits 
running  full  as  calculated  by  Kutter's  formula  n  —  .013.  By 
the  use  of  the  multipliers  given  on  Part  1  of  this  diagram  it  can 


HYDRAULIC  DIAGRAMS   AND   TABLES  79 

also  be  used  for  values  of  n  of  .012,  .014,  and  .015.  These  diagrams 
may  be  used  for  calculating  the  discharge  of  pipes  when  the 
Kutter  formula  is  preferred  for  this  purpose,  but  this  formula  is 
known  to  give  erroneous  results  for  pipes  and  Figs.  30,  31, 
and  32  are  preferable  for  this  purpose.  The  diagram  is 
intended  principally  for  calculating  the  flow  in  circular  chan- 
nels partly  full  by  the  use  of  Table  22  in  connection  with 
the  diagram.  The  diagram  gives  the  flow  when  the  pipe  is 
just  full  and  the  table  gives  the  multipliers  for  discharge  and 
velocity  to  reduce  the  same  to  the  flow  when  the  same  pipe 
or  circular  conduit  is  flowing  at  any  proportional  depth. 
To  illustrate  the  use  of  the  diagram  and  table,  several  examples 
will  be  cited: 

Problem:  Find  the  discharge  and  velocity  of  a  circular  conduit 
6  feet  in  diameter  flowing  at  depth  of  .25  times  the  diameter 
on  a  slope  of  .003  or  3  feet  per  1,000. 

Solution:  From  Fig.  22  read  the  discharge  237  c.  f.  s.  and  velocity 
8.4  feet  per  second.  These  figures  are  for  the  pipe  flowing 
full.  From  the  table  find  the  multipliers  for  proportional 
depth  of  0.25  and  diameter  of  6  feet  to  be  .694  for  the  velocity 
and  .136  for  the  discharge.  The  velocity  and  discharge  for 
this  pipe  flowing  0.25  full  on  a  slope  of  .003  then  are: 

V  =  .694  X  8:4  =  5.8  feet  per  second, 
and  Q  =  .136  X  237  =  32.2  c.  f.  s. 
Problem:    In  the  above  pipe  what  would  be  the  discharge  and 

velocity  if  n  =  .015? 

Solution:  The  table  on  Fig.  22,  Part  1,  gives  the  multiplier  for 
n  =  .015  as  .856.  The  discharge  would,  therefore,  be 
32.2  X  .856  =  27.5,  and  the  velocity  would  be  5.8  X  .856  =  5. 
Problem:  300  c.  f.  s.  is  to  be  carried  in  an  8-foot  diameter  con- 
duit on  a  grade  of  .004,  or  4  feet  per  1,000  n  =  .013.  How 
deep  will  it  flow  and  at  what  velocity  ? 

Solution:  From  Fig.  22  read  the  discharge  of  an  8-foot  conduit 
flowing  on  a  slope  of  4  feet  per  1,000  as  590  c.  f.  s.;  the  corre- 
sponding velocity  being  11.7.  The  ratio  of  given  discharge  to 

"full"  discharge  is  —  =  .517.     Enter  the  table  with  this 

OoU 

multiplier,  and  find  that  it  corresponds  to  a  depth  of  flow  of 


80  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

0.51  times  the  diameter.  The  multiplier  of  the  velocity  is 
observed  to  be  between  1.008,  1.009,  and  the  velocity,  there- 
fore, is  11.7  X  1.0085  =11.8  feet  per  second. 

Problem:  In  the  above  problem  what  would  be  the  depth  of 
flow  and  velocity  for  n  —  .015? 

Solution:  The  discharge  and  velocity  for  n  —  .013  are  read  as 
before  to  be  590  and  11.7  respectively.  The  multiplier  for 
n  =  .015  for  a  diameter  of  8  feet  is  read  from  the  table  on 
Part  1  to  be  .859.  The  discharge  and  velocity  for  n  =  .015 
are,  therefore,  590  X  .859  =  506  and  .859  X  11.7  =  10,  re- 
spectively. The  ratio  of  given  discharge  to  full  discharge  is 

300 

TTT  =.593.     Enter  the  table  with  this  multiplier  and  find 

ouo 

that  it  corresponds  to  a  depth  of  flow  of  about  .553  times  the 
diameter.  The  multiplier  for  velocity  is  observed  to  be 
about  1.04,  and  the  velocity,  therefore,  is  10.4. 
Figs.  23  and  24  give  discharges  directly  for  various  sizes  of 
rectangular  wooden  flumes  with  different  depths  of  water  flowing 
therein.  They  cover  the  sizes  commonly  used  on  small  sublaterals. 
Fig.  23  covers  the  smaller  slopes,  while  Fig.  24  covers  the  steeper 
slopes,  such  as  are  commonly  termed  chutes.  The  discharges 
for  three  different  depths  of  flow  in  the  flume  are  given  in  each 
case,  and  interpolations  may  be  made  for  other  depths.  The 
flumes  are  assumed  to  be  constructed  of  lumber  surfaced  on 
one  side  and  one  edge,  and  are  designated  by  their  nominal 
dimensions.  Thus,  by  an  8  X  8  flume  is  meant  one  made  of  8-inch 
boards;  the  width  being  slightly  less  than  8  inches,  due  to  the 
dressed  edge.  The  side  height  is  the  width  of  an  8-inch  5  1  S  1  E 
board  less  the  thickness  of  the  S  1  S  I  E  bottom  board.  The  dia- 
grams may  also  be  used  for  rough  lumber  with  practical  accuracy. 
The  depth  of  side  boards  is  always  stated  first,  thus :  An  8-inch  X 
12  inch  flume  has  a  width  of  slightly  less  than  12  inches  and  an 
outside  depth  of  slightly  less  than  8  inches,  the  inside  depth  being 
equal  to  the  width  of  the  8-inch  S  I  S  1  E  board  less  the  thickness 
of  the  12-inch  S  1  S  I  E  board,  etc. 

Fig.  25  is  used  for  the  design  of  small  canals  in  earth.  It  is 
based  on  the  assumption  of  side  slopes  Ij  to  1,  bottom  width 
equal  to  twice  the  depth  and  a  value  of  n  of  .0225.  Fig.  26 


HYDRAULIC  DIAGRAMS  AND   TABLES  81 

gives  similar  data  for  a  value  of  n  of  .025.  These  diagrams  are 
to  be  used  in  conjunction  with  Fig.  25J  for  the  complete  design 
of  a  canal.  Although  these  diagrams  are  based  on  the  assumption 
that  the  bottom  width  is  equal  to  twice  the  depth,  they  give 
results  with  sufficient  accuracy  between  the  limits  of  b  =  d  and 
b  —  3  d.  Beyond  these  limits  only  approximate  results  are 
obtained.  It  is  probably  safe  to  say  that  a  large  majority 
of  all  earth  canals  of  capacities  up  to  80  c.  f.  s.  have. side 
slopes  of  1J  to  1,  and  are  designed  with  a  value  of  n  of  .0225 
or  .025.  The  usefulness  of  these  diagrams  is,  therefore,  plainly 
evident. 

Figs.  27,  27\,  and  28  are  similar  to  the  above,  but  cover 
on  a  larger  scale  canals  of  capacities  up  to  8  c.  f .  s.  for  which  the 
larger  diagrams  are  difficult  to  read. 

Fig.  29  gives  the  discharge  of  semicircular  steel  flumes. 
The  diagrams  are  based  on  a  value  of  n  of  .012  and  a  freeboard 
(distance  of  water  surface  below  top  of  flume)  of  one-sixth  of 
the  radius.  If  it  is  desired  to  use  other  values  of  n,  or  a 
different  freeboard,  the  multipliers  given  in  Table  23  should  be 
used.  For  example:  the  discharge  of  a  7-foot  flume  on  a  slope 
of  .0008  is  found  from  Fig.  29  to  be  73.5  c.  f.  s.;  this  is  for 
n  =  .012  and  freeboard  of  one-sixth  the  radius,  or  0.583  foot. 
If  the  value  of  n  were  .015  and  the  freeboard  one-tenth  the 
radius,  or  0.35  foot,  we  would  find  under  "  n  =  .015  "  in  the 
table  the  multiplier  0.788  to  transfer  to  the  new  value  of  n, 
and  under  "Freeboard  1/10  R  "  we  would  find  the  multiplier 
for  discharge  1.149  to  transfer  to  this  new  value  of  the  freeboard. 
The  discharge  for  n  =  .015  and  freeboard  =  1/10  R,  or  0.35 
foot,  then,  is  73.5  X  0.788  X  1.149  =  66.5  c.  f.  s. 

It  is  generally  desired  to  know  the  corresponding  velocity 
also.  This  is  derived  from  the  known  discharge  and  area.  The 
area  of  water  section  corresponding  to  different  freeboards  is 
given  in  the  table.  Thus,  we  find  for  the  case  in  question,  the 
area  with  freeboard  of  1/10  R  is  16.8,  and  dividing  this  into  the 
discharge  66.5  we  get  a  velocity  of  3.96  feet  per  second. 

Table  23  gives  the  various  elements  corresponding  to  only 
four  different  depths  of  flow,  viz :  .417  D,  .437  D,  .45  D,  and  .458  D. 
This  will  ordinarily  be  sufficient  for  designing  purposes,  but  it 


82  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

is  frequently  desired  to  know  the  velocity  and  discharge  for  other 
depths,  and  these  may  be  obtained  by  the  use  of  Table  24.  For 
example:  Find  the  discharge  and  velocity  for  a  12  foot  1  inch 
flume  flowing  with  a  depth  of  3  feet  when  the  discharge  of  the 
same  flume  flowing  at  a  depth  of  0.417  D  is  given  by  the  diagram 
as  300  c.  f  .  s.  and  the  velocity  is  given  as  6.6  feet  per  second.  A 
depth  of  3  feet  corresponds  to  .248  D.  Enter  the  table  under 
D  =  10  feet,  as  the  multipliers  for  larger  diameters  are  practi- 
cally the  same,  and  find  on  the  horizontal  line  marked  .25  D  the 
multiplier  for  velocity  =  .758,  and  the  multiplier  for  discharge 
=  .376.  The  correct  values  are  somewhat  less  than  this  and  are 
found  by  interpolation  between  .24  and  .25  to  be  .754  and  .370, 
respectively.  The  velocity  in  the  12  foot  1  inch  flume  flowing 
with  the  depth  of  3  feet  is,  therefore,  .754  X  6.6  =  5  feet  per 
second,  and  the  corresponding  discharge  is  300  X  .370=  111  c.  f.  s. 
This  table  is  also  convenient  when  it  is  desired  to  obtain  the 
depth  of  flow  corresponding  to  a  given  discharge.  Example: 
The  discharge  of  a  10  foot  2  inch  flume  flowing  with  a  freeboard 
of  1/6  R  is  250  c.  f.  s.;  at  what  depth  will  this  flume  flow  when 

100 
discharging  100  c.  f.  s.?    The  ratio  of  these  quantities 


.400;  in  the  last  column  of  the  table  we  see  that  a  depth  of  .26  D 
gives  the  multiplier  for  discharge  .407;  the  flume  will,  therefore, 
flow  at  a  depth  of  slightly  less  than  .26  D  or  2.65  feet;  also  the 
multiplier  for  velocity  is  found  to  be  slightly  less  than  .776,  and 
this  multiplied  by  the  velocity  corresponding  to  a  flow  of  250 
c.  f.  s.  gives  the  velocity  for  a  flow  of  100  c.  f.  s. 

Figs.  30,  31,  and  32  give  the  discharge  of  wood  stave,  cast 
iron,  riveted  steel,  and  concrete  pipes  based  on  the  formulas 
given  on  page  67. 

Fig.  33  gives  the  relative  velocities  and  slopes  corresponding 
to  different  values  of  n.  There  are  two  sets  of  curves  on  the 
diagram,  the  one  showing  the  variation  of  velocity  and  discharge 
(left  scale)  and  the  other  the  variation  of  the  slope  (right  scale). 
The  right  and  left  scales  give  directly  the  comparison  of  other 
values  of  n  with  n  =  .010.  For  a  comparison  of  any  other  two 
values  of  n  it  is  necessary  to  read  two  figures  from  the  diagram 
and  obtain  their  quotient.  For  example:  suppose  it  is  desired 


HYDRAULIC  DIAGRAMS  AND   TABLES  83 

to  know,  other  things  being  equal,  what  is  the  relative  slope  of  a 
canal  having  a  hydraulic  radius  of  2  for  values  of  n  of  .02  and  .025. 
For  n  =  .02  the  slope  compared  with  n  —  .01  is  0.415  and  for 
n  —  .025  the  corresponding  figure  is  0.660.  The  ratio  of  the  two 
or  0.66  -r-  0.415  =  1.6  shows  that  the  slope  for  n  =  .025  must 
be  1.6  times  as  great  as  for  n  =  .020.  The  relative  discharges 
are  similarly  found  to  be  0.482  and  0.382,  showing  that  the 

0  S82 
discharge  for  n  =  .025  is  only  ^~  -  =  0.8  as  great  as  for  n  = 


.020,  other  things  being  equal. 

Fig.  34  shows  the  relation  between  head  and  velocity  given 

F2  /  - 

by  the  equation  H  =  1  /  C2  —  or  V  =  C  ^2  g  H.      (  The    value 

of  C  as  used  here  is  the  coefficient  of  discharge,  although  it  is 
applied  to  the  velocity.) 

Fig.  35  gives  the  discharge  of  sharp-edged  submerged  orifices 
for  various  areas  of  opening  calculated  from  the  formula  Q  = 
0.61  A  V2  g  H.  This  diagram  is  applicable  to  measuring  orifices, 
and  to  small  sluice  openings  when  the  multipliers  given  below 
the  diagram  are  used.  These  multipliers  are  the  average  val- 
ues obtained  from  a  series  of  experiments  made  at  the  Univer- 
sity of  Wisconsin.  The  results  obtained  from  the  Wisconsin 
experiments  are  given  in  full  in  Table  20. 

The  forms  of  entrance  and  outlet  used  for  the  tubes  in  these 
experiments  were  as  follows  : 
A.   Entrance:  all  corners  90  degrees. 

Outlet:   tube  projecting  into  water  on  down-stream  side  of 
bulkhead. 

a.  Entrance:  contraction  suppressed  on  bottom. 

Outlet:   tube  projecting  into  water  on  down-stream  side  of 
bulkhead. 

b.  Entrance:   contraction  suppressed  on  bottom  and  one  side, 
Outlet:  tube  projecting  into  water  on  down-stream  side  of 

bulkhead. 

c.  Entrance:  contraction  suppressed  on  bottom  and  two  sides. 
Outlet:   tube  projecting  into  water  on  down-stream  side  of 

bulkhead. 
c'.    Entrance:  contraction  suppressed  on  bottom  and  two  sides. 


84 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Outlet:    square  corners  with  bulkhead  to  sides  of  channel 

preventing  the  return  current  along  the  sides  of  the  tube. 

d.     Entrance :  contraction  suppressed  on  bottom,  two  sides  and  top. 

Outlet:   tube  projecting  into  water  on  down-stream  side  of 

bulkhead. 

TABLE  20 

VALUE  OF  THE  COEFFICIENT  OF  DISCHARGE  FOR  FLOW  THROUGH  HORIZONTAL 

SUBMERGED  TUBE,  4  FEET  SQUARE,  FOR  VARIOUS  LENGTHS,  LOSSES 

OF  HEAD,  AND  FORMS  OF  ENTRANCE  AND  OUTLETS 


Loss  of 
Head, 
in  Feet 

Forms  of 
Entrance 
and 
Outlet 

LENGTH  OF  TUBE,  IN  FEET 

0.31 

0.62 

1.25 

2.50 

5.00 

10.0 

14.0 

VALUE  OF  THE  COEFFICIENT  OF  DISCHARGE 

.05  

A 

a 
b 
c 
c' 
d 

A 
a 
b 
c 
c' 
d 

A 
a 
b 
c 
c' 
d 

A 
a 
b 
c 
c' 
d 

A 
a 
b 
c 
c' 
d 

A 
a 
b 
c 
c' 
d 

.631 
.762 
.740 
.834 

.948 

.611 
.636 
.685 

.772 

.932 

.609 
.630 
.677 
.765 

.936 

.609 
.632 

.678 
.771 

.948 

.610 
.634 
.683 
.779 

.965 

.614 
.639 
.689 

.788 

.984 

.650 
.631 
.628 
.630 
.634 
.639 

.672 
.647 
.644 

.647 
.652 
.660 

.769 
.742 
.769 
.769 

.943 

.718 
.698 
.718 
.718 

.911 

.708 
.689 
.708 
.708 

.910 

.711 
.694 
.711 
.711 

.923 

.720 
.705 
.720 
.720 

.938 
.731 

.807 
.810 
.832 
.875 

.940 

.763 
.771 
.791 

.828 

.899 

.758 
.767 

.787 
.828 

.899 

.768 
.777 
.796 
.838 

.911 

.782 
.790 
.809 
.854 

.928 
.796 

.824 

.927 
.780 

.892 
.779 

.893 
.794 

.906 

.812 

.832 

.838 
.848 
.862 
.890 
.875 
.931 

.795 
.801 
.813 
.841 
.830 
.893 

.794 
.803 
.814 
.839 
.829 
.894 

.809 
.819 
.833 
.856 
.846 
.905 

.828 
.850 

.10  

.15  

.20  

.25  

.30.  

HYDRAULIC   DIAGRAMS   AND   TABLES  85 

There  have  been  no  data  of  value  published  in  regard  to  the 
coefficient  of  discharge  of  large  sluice  openings  such  as  are  used 
in  canal  headworks.  In  the  absence  of  such  data,  a  prediction 
may  be  made  on  the  basis  of  the  Wisconsin  experiments,  on  the 
assumption  that  the  sizes  and  shapes  of  openings  used  in  practice 
have  the  same-  coefficients  as  the  4-foot  square  opening  used  in 
the  experiments.  It  is  a  well-known  fact  that  the  shape  of  the 
opening  has  an  influence  on  the  coefficient  of  sharp-edged  orifices, 
but  to  what  extent  this  is  true  for  openings  such  as  are  used  in 
practice  is  not  known.  It  is  probable  that  the  influence  is  smaller 
rather  than  larger  in  the  latter  case.  On  the  whole,  within  the  lim- 
its of  variation  in  shape  of  any  practical  opening  from  the  4-foot 
square  opening  of  the  experiments,  it  is  probably  safe  to  assume 
that  the  difference  in  coefficients  is  slight,  and,  in  any  case,  this 
must  be  accepted  as  the  best  assumption  that  can  be  made.  By 
studying  this  table  in  connection  with  a  particular  design,  the  most 
probable  value  of  coefficient  of  discharge  can  then  be  arrived  at. 
It  is  a  notable  fact  that  the  coefficient  is  increased  by  the  addition 
of  a  short  tube  projecting  into  the  down-stream  water.  This  fact 
could  well  be  taken  advantage  of  in  the  design  of  headgates.  The 
influence  of  the  tube  is  most  marked  in  the  case  of  the  fully 
contracted  orifice,  due  to  suction  in  the  tube  which  tends  to 
prevent  the  full  contraction  of  the  jet  at  the  entrance.  This 
also  explains  the  difference  in  the  effect  of  the  tube  for  differ- 
ent degrees  of  contraction. 

Figs.  36  and  37  give  the  discharge  of  sharp-edged  Cippoletti 
and  rectangular  weirs,  respectively.  Experiments  have  shown 
that  both  the  Cippoletti  and  the  fully  contracted  rectangular 
weir  give  accurate  results  for  heads  up  to  one-third  the  crest 
length,  but  for  higher  heads  the  results  are  not  accurate.  The 
error  has  been  found  to  vary  from  zero  for  Hi  L  =  1/3,  to  30 
per  cent  for  Hi  L  =  1,  or  head  equal  to  length  of  crest.  These 
diagrams  should,  therefore,  not  be  used  for  heads  greater  than 
one-third  the  length  of  crest.  It  should  be  observed  that  each 
diagram  contains  two  sets  of  lines;  the  lower  scale  of  discharges 
is  applicable  to  the  lower  set,  and  the  upper  scale  to  the  upper 
set.  The  scale  of  "  Heads "  is  applicable  to  both  sets  of 
lines. 


86  WORKING  DATA  FOR   IRRIGATION  ENGINEERS 

From  Fig.  37  may  be  obtained  the  discharges  for  both  sup- 
pressed and  contracted  rectangular  weirs.  The  discharge  of 
suppressed  weirs  is  read  directly.  To  obtain  the  discharge  of  a 
contracted  weir,  the  discharge  of  a  suppressed  weir  is  read  first, 
and  from  this  is  subtracted  the  value  read  from  the  line  marked 
"  Values  of  0.666  #5/2."  In  explanation  of  this:  Francis  formula 
for  contracted  weirs  Q  =  3.33  H3/2  (L  —  0.2  H]  may  be  written 
Q  =  3.33  L  H3/2  -  0.666  H5/2  ;  the  first  part  of  this  equation 
is  the  formula  for  suppressed  weirs,  and  if  the  two  parts  of  the 
equation  are  plotted  independently,  the  difference  between  the 
values  read  from  the  two  plotted  lines  gives  the  solution  of 
the  equation.  Because  the  length  "  L  "  does  not  enter  into  the 
second  part  of  the  equation,  only  one  line  is  necessary  for  all 
values  of  L. 

Figs.  36  and  37  are  applicable  only  to  weirs  having  a  free 
fall,  and  this  should  always  be  obtained  if  possible.  In  case  it 
is  absolutely  necessary  to  make  a  measurement  with  weir  sub- 
merged, the  coefficients  in  Table  25  may  be  used  to  obtain 
approximate  results.  This  table  is  applicable  to  both  diagrams. 
These  diagrams  make  no  allowance  for  velocity  of  approach. 
This  should  be  reduced  to  a  negligible  quantity  wherever  pos- 
sible, but  if  this  cannot  be  done  the  coefficients  in  Table  26 
should  be  used. 

Where  a  considerable  velocity  of  approach  exists  the  sup- 
pressed rectangular  weir  with  Bazin's  formula  gives  more  exact 
results  than  are  afforded  by  the  Cippoletti  or  Francis  formulas. 
The  Bazin  formula  automatically  corrects  for  velocity  of  ap- 
proach by  having  inserted  in  the  formula  the  height  of  weir 
crest  above  bottom  of  approach  channel  as  one  of  the  variables. 
The  discharges  per  foot  of  length  of  weir  calculated  from  his 
formula  are  given  in  Table  28  for  various  heights  of  crest  above 
approach  channel.  Prof.  Richard  R.  Lyman  has  recently  pub- 
lished some  tables  in  a  Bulletin  of  the  University  of  Utah  based 
on  extensive  experiments  made  at  Cornell  University  and  the 
University  of  Utah,  which  probably  give  the  most  accurate  re- 
sults for  the  range  covered.  These  are  given  in  Table  27  and 
are  useful  where  the  greatest  accuracy  is  desired. 

Tables  28A,  28B,  and  28C   give   multipliers  to  be  used  in 


HYDRAULIC  DIAGRAMS  AND  TABLES  87 

connection  with  Table  28  to  obtain  the  discharge  over  broad- 
crested  weirs  such  as  are  used  for  diversion  dams. 

Table  29  gives  the  number  of  acre-feet  equivalent  to  a 
given  number  of  second-feet  flowing  for  a  given  length  of  time. 

Fig.  38  is  used  for  converting  a  given  depth  of  water 
applied  to  land  in  a  given  number  of  days  into  terms  of 
number  of  acres  supplied  by  one  second-foot.  These  are  the 
two  terms  in  which  "  duty  of  water  "  is  usually  expressed,  and  a 
simple  means  of  transposing  one  into  the  other  is  very  useful. 

Table  30  contains  a  list  of  hydraulic  formulas  for  convenient 
reference. 


88 


WORKING  DATA  FOR   IRRIGATION  ENGINEERS 


Suggestion : 

n  =  .010  for  straight  and  regular  channels  lined  with 
matched  planed  boards;  neat  cement  plaster;  and  glazed,  coated, 
and  enamelled  surfaces  in  perfect  order. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C  ^~PTs 


Si 

-OPE 

.00005 

.0001 

.0002 

.0004 

.001 

.  01  and  over 

0.1.  . 

67 

78 

85 

89 

94 

95 

0.2  

87 

98 

105 

110 

113 

114 

0.3  

99 

109 

116 

120 

124 

125 

0  4 

109 

119 

125 

129 

131 

133 

0.6 

122 

131 

138 

140 

142 

143 

0  8 

133 

140 

145 

148 

150 

151 

1.0  
1.5  
2.0. 

140 
154 
164 

147 
159 
168 

151 
162 
170 

154 
164 
170 

155 
165 
171 

156 
165 
171 

3.0  
4.0  
6  0 

178 
187 
199 

178 
186 

1Q£ 

179 
185 
193 

179 
184 
191 

179 
184 
190 

179 
184 
190 

10 

212 

205 

201 

199 

197 

196 

20.  . 

228 

216 

210 

207 

205 

204 

HYDRAULIC   DIAGRAMS   AND   TABLES 


89 


Slope 


2 


1  1  1  1  1  1  1  1  1  1 

/ 

~~?~    ~/ 

/    / 

/ 

t\\\  \\y\\ 

/ 

'     / 

Z.7. 

/  , 
z 

/ 

i 

1 

/ 

/ 

/  / 

// 

/ 

/ 

tJ.2 

\       i 

-    '      -,.004 

1  r 

/ 

7    ~t_ 

'  / 

/ 

/  z  > 

/  '   / 

I 

i   2 

L/Z 

'  / 

/ 

/  , 

?  7  / 

L       i 

1 

,^7 

TV 

/ 

/ 

/ 

7       ?     r005 

/ 

, 

/ 

/  /_] 

/V 

/ 

1 

/  / 

i 

7  /  7     / 

y 

/ 

/ 

7     '  r 

/// 

'  / 

/ 

>/ 

?    y         7                     > 

^    ^    r006 

/ 

/ 

/ 

/ 

/  /7 

v/ 

7 

/ 

/ 

'  i 

?     /    7 

z_ 

/ 

f 

777 

^/v 

/ 

/ 

/    y 

.  '  .  Z.       008 

/ 

/ 

/ 

V// 

/  // 

Z 

7 

'     /     y 

...L..L..L 

?';£    a 

.5     1  - 

-^ 

/ 

-A 

/ 

^55v 

^-^-7 

L-/ 

/ 

•  7 

'     t    *    .2- 

^    ---  .015M 

'       'ft 
/ 

/ 

/ 

/ 

/ 

/    / 

/ 

—/- 

--»<---  .02 

t       / 

/  / 

7           ^     y 

^^  ^ 

I 

;  ^ 

f          /  / 

// 

/ 

/ 

/ 

/         ^ 

,/    y 

-  Z-, 

/     '  / 

/ 

/ 

/ 

/  y  , 

/ 

/ 

'  7 

/'        // 

/ 

/ 

?_,  _1 

/        /    // 

/ 

/ 

/ 

7  22 

/ 

/ 

^.7  /  "    Z" 

/  \ 

/ 

/  . 

y 

^  /  / 

/ 

/ 

'  <     [2 

/ 

/ 

/ 

/ 

y 

/ 

/ 

, 

/            ^      (. 

?ji,  ,  ,  E 

/ 

/ 

/ 

^        / 

?        .04 

/ 

/ 

y 

/ 

7          i 

/ 

/ 

7      / 

/       / 

'  /     •     V 

/ 

/ 

/ 

y 

7     "y 

/ 

r 

9     -  -  2  .    ?  J  > 

I1    ^             I// 

/ 

/ 

^ 

/        / 

/ 

'     ^ 

/   '   /  /      // 

/ 

/ 

r    i     ~} 

'   1           '/ 

/ 

2 

/ 

f                7 

/   / 

/ 

lii.ii  i     / 

^ 

A 

^        / 

/     / 

/ 

7     -  1  ,1  .  I  .  f  (  . 

*   t     '           / 

2 

/ 

f 

2 

} 

/ 

2 

-I-|!|   i      A 

/ 

/ 

^    / 

5    t-'tj-t- 

;.iii  !  5 

Z 

/ 

t-/  4 

/ 

2 

J<i  I  S 

/ 

'  / 

'  / 

/ 

7 

5         ^  J  _  ,_  -^-L 

,  Z 

/ 

/ 

7   , 

/  / 

/ 

^:     Z 

/ 

/ 

/     / 

/ 

/ 

/ 

/ 

.3  ii-;!:j: 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

.25  l/tfflW 
.2    -Z-L... 

—f 

/ 

t 

~^-  — 

/  - 

-/ 

7 

\ 

2         2.5       3      3.5    4  5         6       7      8      9    10  15  20         25       30      35 

Velocity,  ( feet  per  second ) 

FIG.  4. 


90 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


Suggestion: 

n  —  .012  for  straight  and  regular  channels  lined  with  un- 
planed  timber  carefully  laid,  sand  and  cement  plaster,  best  and 
cleanest  brickwork,  very  smoothly  finished  concrete  made  with 
steel  forms,  and  smooth-jointed  galvanized  steel  flumes. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C  \/  R  S 


SL 

OPE 

.00005 

.0001 

.0002 

.0004 

.001 

.01  and  over 

0.1. 
0  2 

52 
68 

60 
76 

65 
83 

69 

87 

73 

89 

74 
90 

03  

79 

87 

92 

96 

98 

100 

04  

88 

95 

100 

104 

105 

107 

0.6  

98 

105 

111 

113 

115 

116 

0.8  

107 

114 

118 

121 

122 

123 

1  0 

114 

120 

123 

125 

127 

128 

1  5 

126 

130 

133 

135 

136 

136 

2.0  
30. 

135 
148 

138 
149 

140 
149 

141 
149 

142 
149 

142 
149 

4.0  

156 

155 

155 

154 

154 

154 

6.0  

168 

164 

162 

161 

160 

160 

10.0  

181 

174 

170 

168 

167 

166 

20  0 

196 

185 

180 

176 

175 

173 

HYDRAULIC   DIAGRAMS   AND   TABLES 


91 


Slope 


2.5       3     3.5    4  5         6       7      8     9    10  15 

Velocity,  (feet  per  second) 

FIG.  5. 


20         25        30     35 


92 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


Suggestion : 

n  =  .013  for  straight  regular  channels,  lined  with  concrete 
having  a  steel  trowelled  surface  in  good  order. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C  \/  R  S 


Si 

.OPE 

K. 

.00005 

.0001 

.0002 

.0004 

.001 

.  01  and  over 

0  1 

47 

54 

59 

62 

65 

66 

0  2 

62 

69 

74 

78 

81 

81 

0.3  
0.4  
0.6  

08 

71 

79 
90 
98 

78 
86 
96 
103 

83 
91 
100 
107 

87 
94 
103 
110 

89 
96 
104 
111 

90 
98 
106 
112 

1.0  
1.5  

104 
116 

109 
120 

113 
122 

115 
124 

116 
124 

117 
125 

2.0  
3.0  

124 
136 

127 
137 

129 
137 

130 
138 

130 
138 

130 
138 

4.0  

145 

143 

143 

142 

142 

142 

6  0 

156 

152 

150 

149 

149 

148 

10.0  
20  0. 

169 
184 

162 
173 

158 
168 

157 
164 

155 
163 

154 
161 

HYDRAULIC   DIAGRAMS   AND   TABLES 


93 


Slope 


t 

/  // 

t 

t 

/ 

/ 

)      

-/- 

-f 

-/ 

— 

~f  f 

*—f 

t 

~t-~j-  '  —  / 

_  .  ^  -    -    -  f  .    .   ^QQg 

1 

/ 

/ 

1  /  / 

/ 

/ 

f 

/7              ?~ 

.L.  ..  . 

"i!:::    Z 

-j 

r 

/ 

v/ 

^i-f 

/ 

// 

/ 

/ 

-L                1 

/        * 

/ 

/ 

/ 

/ 

/ 

/  7 

/ 

/ 

'L       7     L 

2 

7 

/ 

. 

f 

1      / 

>  / 

V 

/ 

1 

7      t    £ 

^      y              ? 

^        y 

/ 

/ 

/ 

/ 

/  / 

// 

1 

/ 

/ 

/ 

/       '    r010 

/ 

^    2_ 

/ 

/ 

/ 

/ 

/ 

/ 

'/  / 

// 

/ 

/ 

f 

i 

7    ^/     ^ 

/        /     , 

'  / 

/ 

/ 

/ 

/ 

/// 

'/' 

/ 

'  t 

L     ^  / 

/  /• 

;              _-z  

/   ;;;  2. 

jfij  tgi  /y 

t/ 

\ 

7 

/ 

=£ 

<_.^.  ...,,.  015 

5.5    -^  —  -±- 

5    ::;z.:j?:: 

v 

//. 

/- 

/ 

V 

1 

7 

7  "7 

" 

--/- 

it 

/ 

z 

/ 

/ 

^    r-~-'-'/-'- 

2  r     -.04 

-         t       7    y_L 

^  ///  '  '/  f  / 

/  / 

/ 

^     (  '     r05 

///  /  /  // 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

<f  '     t      t 

1    /    /   / 

/z'i  1  2 

/ 

/ 

/ 

/ 

-77       > 

/      * 

^     ^    ^' 

j!  /  i!!i  2 

7 

/ 

/ 

/ 

7 

7  ~~f 

/ 

Z      ^       L 

/    i 

it    '>    ' 

/  /// 

/ 

/ 

/ 

/ 

/ 

7       / 

/    //*/ 

^  ^V'V  7. 

~/ 

/  / 

/ 

/ 

/  / 

/ 

/ 

X       7     / 

/ 

/ 

/ 

/ 

/ 

/ 

Q        Z  ^      ^  ^     J 

/  /  .     '  / 

/  / 

/ 

^ 

7     ^ 

»y        *  7_  * 

'  1  1  t  /  f 

/ 

/ 

/ 

^   / 

Z     ^     ' 

'tt  /  ,  / 

f 

/ 

/ 

/ 

/ 

/ 

J.       L      ^ 

^  i       >     /   '  / 

/ 

/ 

^ 

i       ^ 

/  /  /  7  / 

/      /      i   // 

/ 

/ 

/ 

}     / 

/ 

/ 

~/     j      7 

/     /    /  / 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

'*/  ''       ~2_ 

/ 

/ 

/ 

/ 

/ 

/ 

'    / 

j  '/    s  / 

/    t   /           / 

/ 

"7 

/ 

/ 

/ 

S 

/ 

1 

y 

?/           /      / 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

.3    ?Z--::;Z: 

.25  ---/--7Z- 
.2   t--l..l.t 

~y  >Tn"    / 

\ 

Y~ 

/ 

/ 

Y  ~ 

2         2.5       3      3.5     4  5         6       1      8     9   10  15  20         25       30     35 

Velocity,  (feet  per  second) 

FIG.  6. 


94 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


Suggestion: 

n  =  .014  for  straight  regular  channels,  lined  with  concrete, 
having  a  wooden  trowelled  surface  in  good  order. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C  ^Ws 


Si 

OPE 

.00005 

.0001 

.0002 

.0004 

.001 

.  01  and  over 

0  1 

43 

49 

53 

56 

59 

60 

0  2. 

56 

63 

67 

71 

73 

74 

0  3  . 

65 

72 

76 

79 

81 

83 

0.4  
0.6  

72 
82 

79 

88 

83 
92 

86 
95 

88 
96 

89 
98 

0.8  

90 

95 

99 

101 

102 

103 

1.0  

96 

101 

104 

106 

107 

108 

1.5  

107 

111 

113 

114 

115 

116 

2.0  

115 

118 

119 

120 

121 

121 

3  0 

127 

127 

128 

128 

128 

128 

4.0.  . 

135 

134 

133 

133 

133 

132 

6.0.  .  .  . 

146 

142 

140 

139 

139 

138 

10.0  

158 

152 

148 

146 

145 

145 

20.0  

174 

163 

158 

154 

153 

152 

HYDRAULIC  DIAGRAMS  AND   TABLES 


95 


4 

3.5 

3 

2.5 

J2 

ii.5 


-01 

w  .j 


.25 


Slope 


s     a 


~ 
§ 


^/£ 


/// 


.OOG 


.008 


;.OJ 


.015, 


.02 


2         2.5        3     3.5     4  5         6        7      8     9    10  15  20         25       30      35 

Velocity,  (feet  per  second) 


FIG.  7. 


96 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


Suggestion: 

n  =  .015  for  straight  and  regular  channels  of  ordinary 
brickwork,  smooth  stonework,  rough  concrete  work,  and  foul 
and  slightly  tuberculated  iron. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C  ^R~S 


SL 

OPE 

.00005 

.0001 

.0002 

.0004 

.001 

.01  and  over 

0.1  . 

39 

44 

48 

50 

54 

54 

0.2  
0.3  
0  4 

51 

59 
66 

57 
65 

72 

61 
69 
76 

65 
73 
79 

66 

74 
80 

67 
76 

82 

0  6 

76 

81 

85 

87 

88 

90 

0.8  

83 

88 

91 

93 

94 

95 

1.0  

89 

93 

96 

98 

99 

99 

1.5  

99 

103 

105 

106 

108 

107 

2.0  

107 

109 

111 

112 

112 

112 

3.0  

118 

119 

119 

119 

119 

119 

4.0  
6.0  
10.0  

126 
137 
149 

125 
134 
143 

125 
132 
140 

124 
130 
138 

124 
130 
136 

123 
129 
136 

20.0  

165 

154 

149 

146 

144 

143 

HYDRAULIC  DIAGRAMS  AND   TABLES 


97 


Slope 


10 


2.5        3     3.5     4 


5         678910  15 

Velocity,  (feet  per  second) 
FlG.  8. 


20         25       30     35 


98 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


Suggestion: 

n  =  .020  for  channels  of  compact  sand  and  fine  gravel, 
rough  set  rubble,  ruined  masonry,  rough  tuberculated  iron,  and 
canals  in  earth  in  good  condition  lined  with  well-packed  gravel, 
partly  covered  with  sediment,  and  free  from  vegetation. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C  ^l~R~S 


SL 

OPE 

.00005 

.0001 

.0002 

.0004 

.001 

.01  and  over 

0.1  
0  2 

26 
35 

30 
39 

32 
42 

34 
44 

36 
45 

36 
46 

0  3 

41 

45 

48 

50 

51 

52 

0.4  
0  6 

46 
53 

50 
57 

53 
60 

55 

62 

56 
63 

57 
64 

08  

59 

63 

65 

67 

68 

68 

1.0  

64 

67 

69 

70 

71 

72 

1.5  

72 

75 

77 

78 

78 

79 

2.0  

79 

81 

82 

83 

83 

83 

3  0 

88 

89 

89 

89 

89 

89 

4  0 

95 

94 

94 

94 

93 

93 

6  0 

105 

102 

100 

99 

99 

99 

10  0  

116 

111 

108 

107 

105 

105 

20.0  

131 

122 

117 

115 

113 

112 

HYDRAULIC  DIAGRAMS  AND  TABLES 


99 


Slope 


§§§< 


)    I 

9 

z_. 

...  :;L  ...,^ 

/ 

/ 

y 

/ 

/ 

A? 

•f—j 

- 

y* 

,.004 

3 

/           /      / 

/ 

f 

f 

f 

:             J 

f 

f 

/ 

7 

6 

5 

/        y       /     / 

I 

/ 

f 

/* 

/ 

/          / 

l 

^                 ^1 

/'     y    / 

/ 

/ 

/ 

t 

/ 

/ 

7_ 

V 

/ 

.006 

^       f      IZ 

/ 

/ 

f 

/ 

/     /    Jf 

/ 

/ 

y             / 

^       '      '    r   / 

/  1 

/ 

/ 

/ 

/ 

/ 

~{~7 

/ 

i 

7 

L  '       / 

i  i!    i!2 

// 

/ 

/ 

/ 

/( 

/ 

/ 

.  ' 

,  .008 

/           /  •"]' 

/  ^  ^J2 

/ 

/ 

/ 

/ 

y 

/ 

1 

/ 

. 

-   010 

yM/i4  Mi/rLr  A  / 

% 

g 

% 

iz 

11.02 

2 
1.5 

1 

.9 
.8 

.7 

.6 
.5 

.4 
.35 

.3 
.25 

.2 

/ 

2 

/ 

~t-. 

Z   Z!^  ^  2t-t 

III 

1 

/ 

-/ 

/ 

^ 

? 

\ 

7' 

tn 

t 

/ 

4 

•  |T 

--.03 
--.04 

/ 

j.   ^7  /  1  i~i  ^ 

//  'E7    71 

/ 

/, 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

y/-/ 

'777/  /  ^^^ 

/   '  /  >  ' 

/ 

/ 

/ 

/ 

f 

/ 

Z 

/ 

y 

y.05 

/ 

/ 

^ 

///y    /  /  /  // 

t    i  ' 

' 

/ 

f 

f 

/ 

/ 

y 

t 

/    / 

///   7  £  7  /  / 

/  '  /  '      / 

/ 

/ 

/ 

f 

/ 

'     > 

/ 

/ 

/ 

/V 

//  j.  '  cL  /  ' 

/  //       / 

/ 

/ 

/ 

/ 

'  / 

* 

/ 

f 

7-              L-  >           ' 

/ 

/* 

~/~ 

y 

/ 

Z2       Z   j     ' 

/*  /           "/ 

/ 

/ 

/ 

2 

^ 

/   / 

y       '77         * 

^  '      ^     / 

/ 

y 

y 

/ 

/ 

\  / 

'7*  7.7.7-  f  S  ^ 

/      /    i  / 

/ 

2 

/ 

,y 

/ 

/ 

f       / 

7  /  /  /      y      y          / 

/     f    / 

/ 

y 

/ 

~7 

/ 

/ 

/  / 

/~/2.    *    \    \    ^ 

'    tr    '  / 

/ 

/ 

/ 

/ 

f  / 

, 

j  J)   >  5  /  7 

.'    /  ,  / 

/ 

/ 

/ 

/ 

/   y 

/ 

/ 

/ 

2    *  ^  ^ 

/    /  /       i 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/// 

2  *j  .'    ^? 

t    >  /  A 

/ 

/ 

/ 

2 

?  / 

/ 

/ 

/ 

// 

/  .'  />     / 

>     '   '        / 

/ 

/ 

'  / 

/ 

y 

'  / 

'      / 

{-J.JL                 *        ' 

/  /    /'  / 

/ 

/ 

/ 

/ 

& 

/_/          ^      y      / 

:j:j!:jj:jj    ^ 

1 

/ 

\{ 

—  r/ 
1 

.5            2         2.5 

3     3.5     4 

Velocity,  (f< 

jet 

'-> 
pe 

rs 

3 
6( 

JO 

7 
U( 

1) 

i 

10 

15 

20 

FIG.  9. 


100 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


Suggestion : 

n  =  .0225  for  canals  in  earth  in  fair  condition  lined  with 
sediment  and  occasional  patches  of  algae,  or  composed  of  firm 
gravel  without  vegetation.  A  common  figure  for  earth  canals. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C  Bill's 


SL 

OPE 

.00005 

.0001 

.0002 

.0004 

.001 

.  01  and  over 

0  1 

22 

25 

27 

29 

30 

31 

0  2. 

30 

33 

36 

37 

39 

39 

0.3  .... 

36 

39 

42 

43 

44 

45 

0.4  

40 

43 

46 

47 

48 

49 

0.6  

46 

50 

52 

54 

55 

55 

0.8  

52 

55 

57 

58 

59 

60 

1.0  

56 

59 

60 

62 

62 

63 

1.5  

64 

66 

67 

68 

69 

69 

2  0 

70 

71 

72 

73 

73 

74 

3.0  
4.0  

79 

85 

79 

84 

79 
84 

79 
84 

79 

83 

79 

83 

6.0  

94 

92 

90 

89 

89 

88 

10  0 

105 

100 

98 

96 

95 

94 

20  0 

120 

111 

106 

104 

102 

101 

HYDRAULIC  DIAGRAMS  ANIV  TABLES 


10 


4 

3.5 

3 
2.5 


1.5 


g 

*P  1 

S   .9 


.25 


Slope 

"^^lO   CO  f*C 


iilii   i  i 


IS 


z 


// 


006 


010 


1.5  2         2.5       3     3.5    4  5        6       7      8     9   10 

Velocity,  (feet  per  second) 


15  20 


FIG.  10. 


102 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Suggestion: 

n  =  .025  for  canals  in  earth  of  tolerably  uniform  cross- 
section,  slope  and  alignment  in  average  condition, — the  water 
slopes  being  lined  with  sediment  and  minute  algae,  or  com- 
posed of  loose,  corirse  gravel;  and  for  very  smooth  rock  sections. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C  "^  RS 


R 

SLOPE 

.  00005 

.0001 

.0002 

.0004      .001 

.  01  and  over 

0.1  . 

20 
26 

31 
35 
41 

46 
49 
57 
62 
71 
77 
85 
96 
110 

22 
29 
34 
38 
44 
48 
52 
59 
64 
71 
76 
84 
92 
102 

24 
31 
36 
40 
46 
50 
54 
60 
64 
72 
76 
82 
89 
98 

25 
32 
37 
42 
47 
51 
55 
61 
65 
71 
76 
81 
88 
96 

27 
34 
39 
43 
48 
52 
56 
62 
66 
71 
75 
81 
87 
94 

27 
34 
39 
44 
49 
53 
56 
62 
66 
71 
76 
81 
86 
93 

0.2  

0.3  

0  4 

0.6  
0.8  
1.0  
1.5  

2.0  

3.0  

4  0 

6  0 

10  0  .  . 

20  0  

HYDRAULIC  DIAGRAMS   AND  TABLES 


103 


4 

3.5 

8 

2.5 

1.2 
1.5 


Slope 


ffi 


ft 


ill.ii 


ooc 

008 
010 

015  < 


1.5  2        2.5       3     3J    4          5        6       7      8     9  10 

Velocity,  (feet  per  second) 


15  20 


FIG.  11. 


104 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Suggestion : 

n  =  .030  for  canals  in  earth  in  poor  condition,  having  the 
bed  partly  covered  with  debris,  or  having  comparatively  smooth 
sides  and  bed,  but  the  channel  partly  obstructed  with  grass, 
weeds,  or  aquatic  plants;  and  for  average  rock  sections. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C 


•p 

Si 

OPE 

.00005 

.0001 

.0002 

.0004 

.001 

.  01  and  over 

0.1.. 

16 

17 

18 

19 

21 

21 

0  2  

21 

23 

25 

25 

27 

27 

0.3  

25 

27 

29 

30 

30 

31 

0.4  

28 

31 

32 

33 

34 

35 

0.6  

33 

35 

37 

38 

39 

39 

0.8  

37 

39 

41 

42 

42 

43 

1  0  

40 

42 

44 

45 

45 

45 

1  5 

47 

48 

49 

50 

50 

51 

2.0  

51 

53 

54 

54 

54 

55 

3.0  

59 

59 

59 

•  59 

59 

59 

4  0 

64 

64 

63 

63 

63 

63 

6.0  
10.0  
20.0  

72 
82 
96 

71 
78 
89 

69 
76 

85 

69 
75 
83 

68 
74 
81 

68 
74 
80 

HYDRAULIC  DIAGRAMS  AND   TABLES 


105 


Slope 


Sirs   O  to 
£2J32iM         co      •*    ia  «o 
II   1  1  8  §         §§00 


10 

9 

8 
7 

6 
5 

4 

3.5 

3 
2.5 


1.5 


.4 
.35 

.3 

.25 


< 


2         2.5       3     3.5     4  5        6       7       8     9    10 

Velocity,  (feet  per  second) 

FIG.  12. 


008 
.01 

.015 
I 

.«j 

.03 
.04 


15  20 


106 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Suggestion: 

n  =  .035  for  canals  in  earth  in  bad  order  and  regimen,  having 
the  channel  strewn  with  stones  and  detritus  or  about  one-third 
full  of  vegetation;  and  for  rough  rock  sections. 

VALUES  OF  C  IN  THE  FORMULA  V  =  C 


Si 

OPE 

R 

.00005 

.0001 

.0002 

.0004 

.001 

.01  and  over 

01 

13 

14 

15 

16 

17 

17 

02  

18 

19 

21 

21 

22 

22 

0  3  

21 

22 

24 

24 

25 

25 

0.4  

24 

25 

27 

27 

28 

29 

0.6  

28 

30 

31 

31 

32 

33 

0  8 

31 

33 

34 

35 

35 

35 

1  0 

34 

35 

37 

37 

38 

38 

1  5 

40 

41 

42 

42 

43 

43 

2.0 

44 

45 

45 

45 

46 

46 

3.0  

50 

51 

51 

51 

51 

51 

4.0  

56 

55 

55 

55 

54 

55 

6  0 

63 

61 

60 

60 

59 

59 

10  0 

72 

69 

67 

66 

65 

65 

20  0  .    .  .    . 

85 

79 

76 

73 

72 

71 

HYDRAULIC  DIAGRAMS  AND  TABLES 


107 


10 


4 
3.5 


1.5 


ffi 


.35 


.25 


Slope 


Hi 


1.5  2         2.5      3     3.5     4          5        6       7      8     9   10 

Velocity,  (feet  per  second) 


ti=.085 


.015 

.02 


.05 


15  20 


FIG.  13. 


108 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


TABLE  21 
VALUES  OF  C  FOR  USE  IN  THE  CHEZY  FORMULA  V  =  C \/R~S 


\  n 

*\ 

.009 

.010 

.011 

.012 

.013 

.014 

.015 

.017 

.020 

.0225 

.025 

.030 

.035 

.040 

Slope  S  =  .00005  =  1  in  20,000  =  0.264  feet  per  mile 


.1 

78 

67 

59 

52 

47 

43 

39 

33 

26 

22 

20 

16 

13 

11 

.2 

100 

87 

77 

68 

62 

56 

51 

44 

35 

30 

26 

21 

18 

15 

.3 

114 

99 

88 

79 

71 

65 

59 

50 

41 

36 

31 

25 

21 

18 

.4 

124 

109 

97 

88 

79 

72 

66 

57 

46 

40 

35 

28 

24 

20 

.6 

139 

122 

109 

98 

90 

82 

76 

65 

53 

46 

41 

33 

28 

24 

.8 

150 

133 

119 

107 

98 

90 

83 

71 

59 

52 

46 

37 

31 

27 

1.0 

158 

140 

126 

114 

104 

96 

89 

77 

64 

56 

49 

40 

34 

29 

1.5 

173 

154 

139 

126 

116 

107 

99 

87 

72 

64 

57 

47 

40 

34 

2 

184 

164 

148 

135 

124 

115 

107 

94 

79 

70 

62 

51 

44 

38 

3 

198 

178 

161 

148 

136 

127 

118 

104 

88 

79 

71 

59 

50 

44 

*3.28 

201 

181 

164 

151 

139 

129 

121 

106 

91 

81 

72 

60 

52 

46 

4 

207 

187 

170 

156 

145 

135 

126 

111 

95 

85 

77 

64 

56 

49 

6 

220 

199 

182 

168 

156 

146 

137 

122 

105 

94 

85 

72 

63 

56 

10 

234 

212 

195 

181 

169 

158 

149 

134 

116 

105 

96 

82 

72 

64 

20 

250 

228 

211 

196 

184 

174 

165 

149 

131 

120 

110 

96 

85 

77 

50 

266 

245 

228 

213 

201 

190 

181 

165 

148 

136 

127 

112 

101 

93 

100 

275 

254 

237 

222 

210 

200 

190 

175 

158 

146 

137 

123 

112 

104 

Slope  5  =  .0001  =  1  in  10,000  =  0.528  feet  per  mile 


.1 

90 

78 

68 

60 

54 

49 

44 

37 

30 

25 

22 

17 

14 

12 

.2 

112 

98 

86 

76 

69 

63 

57 

48 

39 

33 

29 

23 

19 

16 

.3 

125 

109 

97 

87 

78 

72 

65 

56 

45 

39 

34 

27 

22 

19 

.4 

136 

119 

106 

95 

86 

79 

72 

62 

50 

43 

38 

31 

25 

22 

.6 

149 

131 

118 

105 

96 

88 

81 

70 

57 

50 

44 

35 

30 

25 

.8 

158 

140 

126 

114 

103 

95 

88 

76 

63 

55 

48 

39 

33 

28 

1.0 

166 

147 

132 

120 

109 

101 

93 

81 

67 

59 

52 

42 

35 

31 

1.5 

178 

159 

144 

130 

120 

111 

103 

89 

75 

66 

59 

48 

41 

35 

2 

187 

168 

151 

138 

127 

118 

109 

96 

81 

71 

64 

53 

45 

39 

3 

198 

178 

162 

149 

137 

127 

119 

104 

89 

79 

71 

59 

51 

45 

4 

206 

186 

169 

155 

143 

134 

125 

111 

94 

84 

76 

64 

55 

49 

6 

215 

195 

178 

164 

152 

142 

134 

119 

102 

92 

84 

71 

61 

54 

10 

226 

205 

188 

174 

162 

152 

143 

128 

111 

100 

92 

78 

69 

62 

20 

237 

216 

200 

185 

173 

163 

154 

139 

122 

111 

102 

89 

79 

71 

50 

249 

227 

211 

197 

185 

175 

166 

151 

134 

123 

114 

100 

91 

83 

100 

255 

234 

218 

204 

191 

181 

172 

158 

140 

130 

121 

108 

98 

91 

Slope  S  =  .0002  =  1  in  5,000  =  1,056  feet  per  mile 


.1 

99 

85 

74 

65 

59 

53 

48 

41 

32 

27 

24 

18 

15 

12 

.2 

121 

105 

93 

83 

74 

67 

61 

52 

42 

36 

31 

25 

21 

17 

.3 

133 

116 

103 

92 

83 

76 

69 

59 

48 

42 

36 

29 

24 

20 

.4 

143 

125 

112 

100 

91 

83 

76 

65 

53 

46 

40 

32 

27 

23 

.6 

155 

138 

122 

111 

100 

92 

85 

73 

60 

52 

46 

37 

31 

26 

.8 

164 

145 

131 

118 

107 

99 

91 

79 

65 

57 

50 

41 

34 

29 

1.0 

170 

151 

136 

123 

113 

104 

96 

83 

69 

60 

54 

44 

37 

32 

1.5 

181 

162 

146 

133 

122 

113 

105 

91 

77 

67 

60 

49 

42 

36 

2 

188 

170 

154 

140 

129 

119 

111 

97 

82 

72 

64 

54 

45 

40 

3 

200 

179 

163 

149 

137 

128 

119 

105 

89 

79 

72 

59 

51 

45 

4 

205 

185 

168 

155 

143 

133 

125 

111 

94 

84 

76 

63 

55 

48 

6 

213 

193 

176 

162 

150 

140 

132 

117 

100 

90 

82 

69 

60 

53 

10 

222 

201 

185 

170 

158 

148 

140 

125 

108 

98 

89 

76 

67 

60 

20 

231 

210 

194 

180 

168 

158 

149 

134 

117 

106 

98 

85 

76 

68 

50 

240 

220 

203 

189 

177 

167 

158 

143 

126 

116 

108 

94 

85 

78 

100 

245 

224 

208 

194 

182 

172 

163 

148 

131 

121 

113 

99 

90 

83 

Values  of  C  are  the  same  for  all  slopes  when  R  =  3.28  feet. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


109 


TABLE   21  (Concluded) 
VALUES  OF  C  FOR  USE  IN  THE  CHEZY  FORMULA  V  =  C  \/R~S 


\  n 
£  \ 

.009 

.010 

.011 

.012 

.013 

.014 

.015 

.017 

.020 

.0225 

.025 

.030 

.035 

.040 

Slope  S  =  .0004  =  1  in  2,500  =  2.112  feet  per  mile 


.1 

104 

89 

78 

69 

62 

56 

50 

43 

34 

29 

25 

19 

16 

13 

.2 

126 

110 

97 

87 

78 

71 

65 

54 

44 

37 

32 

25 

21 

18 

.3 

138 

120 

.107 

96 

87 

79 

73 

62 

50 

43 

37 

30 

24 

21 

.4 

148 

129 

115 

104 

94 

86 

79 

68 

55 

47 

42 

33 

27 

23 

.6 

157 

140 

126 

113 

103 

95 

87 

75 

62 

54 

47 

38 

31 

27 

.8 

166 

148 

133 

121 

110 

101 

93 

81 

67 

58 

51 

42 

35 

30 

1.0 

172 

154 

138 

125 

115 

106 

98 

85 

70 

62 

55 

45 

37 

32 

1.5 

183 

164 

148 

135 

124 

114 

106 

93 

78 

68 

61 

50 

42 

37 

2 

190 

170 

154 

141 

130 

120 

112 

98 

83 

73 

65 

54 

45 

40 

3 

199 

179 

162 

149 

138 

128 

119 

105 

89 

79 

71 

59 

51 

45 

4 

204 

184 

168 

154 

142 

133 

124 

110 

94 

84 

76 

63 

55 

48 

6 

211 

191 

175 

161 

149 

139 

130 

116 

99 

89 

81 

69 

60 

53 

10 

219 

199 

183 

168 

157 

146 

138 

123 

107 

96 

88 

75 

66 

59 

20 

227 

207 

190 

176 

164 

154 

146 

131 

115 

104 

96 

83 

73 

66 

50 

235 

215 

198 

184 

173 

162 

154 

139 

123 

112 

104 

91 

82 

75 

100 

239 

219 

203 

189 

177 

167 

158 

143 

127 

116 

108 

96 

87 

80 

Slope  5  =  .001  =  1  in  1,000  =  5.28  feet  per  mile 


.1 

110 

94 

83 

73 

65 

59 

54 

45 

36 

30 

27 

21 

17 

14 

.2 

129 

113 

99 

89 

81 

73 

66 

57 

45 

39 

34 

27 

22 

18 

.3 

141 

124 

109 

98 

89 

81 

74 

63 

51 

44 

39 

30 

25 

21 

.4 

150 

131 

117 

105 

96 

88 

80 

69 

56 

48 

43 

34 

28 

24 

.6 

161 

142 

127 

115 

104 

96 

88 

76 

63 

55 

48 

39 

32 

27 

.8 

169 

150 

134 

122 

111 

102 

94 

82 

68 

59 

52 

42 

35 

30 

1.0 

175 

155 

139 

127 

116 

107 

99 

86 

71 

62 

56 

45 

38 

33 

1.5 

184 

165 

149 

136 

124 

115 

108 

93 

78 

69 

62 

50 

43 

37 

2 

191 

171 

155 

142 

130 

121 

112 

98 

83 

73 

66 

54 

46 

40 

3 

199 

179 

163 

149 

138 

128 

119 

105 

89 

79 

71 

59 

51 

45 

4 

204 

184 

168 

154 

142 

133 

124 

110 

93 

83 

75 

63 

54 

48 

6 

211 

190 

174 

160 

149 

139 

130 

116 

99 

89 

81 

68 

59 

52 

10 

218 

197 

181 

167 

155 

145 

136 

122 

105 

95 

87 

74 

65 

58 

20 

225 

205 

188 

175 

163 

153 

144 

129 

113 

102 

94 

81 

72 

65 

50 

232 

212 

196 

182 

170 

160 

151 

137 

120 

110 

101 

89 

79 

72 

100 

236 

216 

200 

186 

174 

164 

155 

141 

124 

114 

105 

94 

85 

77 

Slope  S  =  .01  =  1  in  100  =  52.8  feet  per  mile 


.1 

110 

95 

83 

74 

66 

60 

54 

46 

36 

31 

27 

21 

17 

14 

.2 

130 

114 

100 

90 

81 

74 

67 

57 

46 

39 

34 

27 

22 

19 

.3 

143 

125 

111 

100 

90 

83 

76 

64 

52 

45 

39 

31 

25 

22 

.4 

151 

133 

119 

107 

98 

89 

82 

70 

57 

49 

44 

35 

29 

24 

.6 

162' 

143 

129 

116 

106 

98 

90 

77 

64 

55 

49 

39 

33 

28 

.8 

170 

151 

135 

123 

112 

103 

95 

82 

68 

60 

53 

43 

35 

31 

1.0 

175 

156 

141 

128 

117 

108 

99 

87 

72 

63 

56 

45 

38 

33 

1.5 

185 

165 

149 

136 

125 

116 

107 

94 

79 

69 

62 

51 

43 

37 

2 

191 

171 

155 

142 

130 

121 

112 

99 

83 

74 

66 

55 

46 

40 

3 

199 

179 

162 

149 

138 

128 

119 

105 

89 

79 

71 

59 

51 

45 

4 

204 

184 

167 

154 

142 

132 

123 

109 

93 

83 

76 

63 

55 

48 

6 

210 

190 

173 

160 

148 

138 

129 

115 

99 

88 

81 

68 

59 

52 

10 

217 

196 

180 

166 

154 

145 

136 

121 

105 

94 

86 

74 

65 

58 

20 

225 

204 

187 

173 

161 

152 

143 

128 

112 

101 

93 

80 

71 

64 

50 

231 

210 

194 

181 

168 

158 

150 

135 

119 

108 

100 

87 

78 

71 

100 

235 

214 

197 

184 

172 

162 

153 

139 

122 

112 

104 

91 

82 

75 

NOTE.— For  slopes  greater  than  .01  C  remains  practically  constant. 


110 


WORKING   DATA  FOR  IRRIGATION   ENGINEERS 


Formulae: 

A    =    0  d 

P  =  b  + 
A_ 
~~P'' 

Q    =   A    V 

Problem  : 


bd 


Water  Surface 


SECTION 


d  =  2.25 

What  is  the  value  of  r  and  what  is  the  value  of  the  dis- 
charge Q  when  V  —  1.5  feet  per  second? 
Solution: 

Enter  diagram  at  depth  =  2.25;  thence  horizontally  to 
6  =  4;  read  r  =  1.06  and  A  —  9;  thence  vertically  to  V  = 
1.5,  and  read  Q  =  13.5. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


111 


»9 

28 

"X  7 


1.5 


A  = 
2.5 


Area  (sq.  feet) 

3        3.5       4  5 


Rectangnli 

6789 


2.5 


2.5 


<^^ 


X 


X 


1  5 


Zx 


st: 


1.5 


2.5         3       3.5       4  5  6         7        8       9     10 

A = Area  (sq.  feet) 


FIG.  14  (Part  1  of  3). — Hydraulic  Elements  of  Rectangular  Sections. 


112 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


Water  Surface 


SECTION 


Formulae: 

A  =  bd 

P  =  b  +  2d 

A  bd 

=  P  ==  b  +  2d 

Q  =  A  V 
Problem: 

Q=  120 

7  =  5.2 

r  =  1.7 

What  is  the  required  bottom  width  b  and  depth  d  ? 
Solution: 

Enter  the  upper  diagram  at  Q  =  120;  thence  horizontally 
to  V  =  5.2;  thence  vertically  downward  to  a  point  half- 
way between  r  =  1.6  and  r  =  1.8,  and  read  b  =  8.5  and 
d  =  2.83. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


113 


15 


20 


A  =  Area 
25       30       35      40  50 


Rectangular 

70     80    90  100 


1.0 


10  15  20 

FIG.  14  (Part  2  of  3).— Hydraulic  Elements  of  Rectangular  Sections. 


25   30   35   40     50    60   70  80  90  100 
A  =Area 


114 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


bd 


Formulae: 
A  = 
P  =  b  + 

A 
r  =  T  = 

Q  =  A  V 


bd 


b+2d 


SECTION 


Problem: 

6  =  850 
V  =  2.2 
b  =  80 

Find  d  and  r. 

Solution: 

Enter  upper  diagram  at  Q  =  850;  thence  horizontally  to 
V  =  2.2;  thence  vertically  downward  to  b  =  80,  and  read 
d  =  4.85  and  r  =  4.32. 

(NOTE. — The  above  values  of  r  and  d  may  be  in  error  by  one  or 
two  figures  in  the  third  digit.  That  is,  r  may  be  4.31  or  4.33, 
and  d  may  be  4.84  or  4.86,  depending  upon  the  personal 
equation  of  the  reader  of  the  diagram.  These  differences, 
however,  are  of  no  practical  importance.) 


HYDRAULIC  DIAGRAMS  AND   TABLES 


115 


A  =Area 

250       300     350 


Rectangular 

400    500   600  700  800  900  1000 


2000 


2.0 


100        150     200    250   300  350  400    500   600  700  800  900 1000 
A  =  Area 

FIG.  14  (Part  3  of  3).— Hydraulic  Elements  of  Rectangular  Sections. 


116 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


Formulae  : 

A  =  b  d  +  0.5  d2 
P  =  b  +  2.24  d 

A_      b  d  +  0.5  d2 
r  ~'=  P   :  =  b  +  2.24  d 
Q  =  A  V 

Problem: 
Q  =  9.2 
A  =  8.5 
ft  =  4 


Water  Surface 


Find  d,  r,  and  F. 


Solution: 


Enter  the  diagram  at  Q  =  9.2;  thence  horizontally  to 
A  =  8.5  and  read  V  —  1.08;  thence  vertically  downward  to 
b  =  4,  and  read  d  =  1.75  and  r  =  1.08. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


117 


1.5 


A=Area 

2.5  3        3.5       4 


Slopes  *4  to  1 

6          7         8      9      1Q 


20     i 

x 

^x 

i 

15 

10 

9   o 

:I 

5  ^ 
4 

3 
2.5 

2 
2 

3 

4 

5 

g 
6  2 

8    0 

•I 

10 

-- 

>-. 

z 

z 

X 

•x 

>  x''; 

;^;:^J<: 

:l  ;i:i;2 

x 

X 

X 

: 

| 

15 

::-7" 

X 

X 

% 

<^-^-, 

.^:.;;x_ 

.x 

2j 

' 

X 

X 

Z 

x 

xx 

x 

x^l 

X 

x 

xi^X. 

X'    --     X 

_X'         ;^ 

12 

xx- 

xx^ 

X- 

x..' 

x'X 

X  - 

10 

Si  9 

X 

x. 

Z 

X 

x 

x 

u 

/ 

X  ^  C 

ijjliiijii 

Jip|:jg 

XX 

xC 

x/ 

'<"' 

x 

/ 

f 

P  6 

as 

4 

3 
25 

? 

z 

^ 

2 

:-  5^^^^x$ 

'.^c','.^^^. 

>^ 

^ 

^ 

^~ 

^^ 

-^ 

7~ 

.  •'•  r 

Z  i 

- 

x 

x' 

x 

X- 

'  X  X  ^  'X  ^   X  X 

X>','Xx 

'X 

/  J 

x 

X 

x 

x 

^ 

~7 

^ 

— 

— 

' 

x 

X^JX  ' 

-xf  :'^ 

•x" 

~x 

x 

X 

'x 

X 

-/ 

-^ 

X 

x 

- 

7 

x 

xp^' 

^/X^X' 

>    ^  "  x  -    OX 

^x 

Xx 

2 

X 

x 

X 

X 

X 

x 

x 

••: 

x 

x 

xx; 

-XXX^^XXJ 

'  !  '  "  I  >:  !2 

Xx 

XJ 

X 

x 

- 

x 

x 

' 

x 

X 

J 

xx; 

•^ 

X 

x 

• 

XXX 

!  *  ',  •  '  x</ 

Sy^l 

x 

x 

^^J 

-  ^ 

x 

-"- 

x  x^ 

x 

• 

X 

X; 

/ 

x 

;  ; 

'x 

x 

? 

x^- 

'.'*,''*''*'' 

-•'xXxx^ 

x/ 

^:J 

x^ 

x 

x- 

x 

x 

X 

x 

4~ 

. 

x 

xx 

X 

g 

x 

< 

/ 

XX^X     i'' 

X/x 

^X 

x 

x 

x 

x' 

- 

2 
3.0 

2.5 
2.0 

f 

1.0 
0.9 
0.8 
0.7 
0.6 

0.5 

X 

'  - 

i 

''- 

• 

x 

/ 

.x 

y 

/ 

X 

y 

/ 

/ 

xy 

X* 

/ 

> 

/ 

X 

^X**^ 

y 

> 

: 

/ 

^x 

y 

>_» 

y 

> 

7 

/ 

x 

/ 

x"^ 

/ 

/ 

y 

1 

/ 

I/ 

x 

/ 

/ 

r 

x 

\, 

/ 

/ 

X 

L 

x 

A 

/' 

/ 

X 

'•b 

/ 

\ 

^' 

\ 

/ 

/ 

> 

^ 

^> 

\ 

^ 

/ 

g'r 

2 

x 

\ 

x 

Q 

/ 

^ 

V 

^K 

/ 

^ 

*i 

<SN 

>• 

X 

^ 

/ij            V 

5 

X' 

x 

<^ 

, 

/ 

^ 

<s 

x 

/ 

Tl  '^ 

x 

x 

x 

x 

?*- 

-^ 

/ 

f 

}/ 

/  < 

/ 

2 

\ 

x 

/ 

/ 

/ 

/ 

x 

1 

/    \ 

/      s/ 

x 

/ 

?C 

/ 

/ 

\ 

> 

•>t     X 

X  "* 

•x^^ 

< 

/ 

/ 

"V 

^ 

x 

\ 

7 

^^^ 

y^ 

"^s 

2 

/ 

x 

/ 

x 

\ 

/ 

/     vsk 

/'<              y 

x 

•/-- 

--X 

f 

x 

/ 

f 

X 

\ 

/ 

/^,.  z_ 

/ 

/ 

/ 

x 

^  ^ 

^ 

/ 

^ 

x        x 

x  —  ^ 

^L 

x 

/ 

x 

^/ 

\ 

x 

'? 

/     / 

7n 

y- 

~v 

' 

\ 

/ 

/ 

/ 

x 

x* 

* 

/ 

*s 

! 

/ 

[ 

x?    /'* 

?<"  -^ 

/ 

/ 

'  / 

/ 

^ 

y 

,? 

/    / 

x  /  ^ 

/ 

/ 

L                        1.5                 2            2.5          3        3.5      4              56789     10 

A=Area 

FIG.  15  (Part  1  of  3). — Hydraulic  Elements  of  Trapezoidal  Sections. 


118  WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


Formulae: 

A    =    b  d  +   0.5  d?  \  Water  Surface 

P  =  b  +  2.24  d 

A        6d  +  0.5d2  \ 


P   ''  ''    b  +  2.24  d  —b *{* 

Q  =  A  V  SECTION  ' 

Problem : 
Q  =  260 
V  =  24 
d  =  1.4 
Find  b  and  r. 

Solution: 

Velocities  over  20  feet  per  second  are  not  indicated  on  the 
diagram,  but  it  can  be  used  for  any  velocity  which,  divided 
into  the  discharge,  will  give  an  area  between  10  and  100 
square  feet,  as  illustrated  in  the  following  solution  of  the 
above  problem. 

If  we  divide  both  Q  and  V  by  10  the  quotient  -y  =  A 

remains  the  same.  We  therefore  enter  the  diagram  with 
Q  =  26  instead  of  260;  thence  horizontally  to  V  =  2.4  in- 
stead of  24;  thence  vertically  downward  to  d  =  1.4,  and 
read  6  =  7  and  r  =  1.05. 

If  V  were  greater  than  26,  say  28,  making  -y  less  than  10, 

we  would  divide  both  Q  and  V  by  100  and  use  Fig.  12,  enter- 
ing the  diagram  with  Q  =  2.6  and  V  =  0.28.  The  remain- 
ing steps  would  be  the  same  as  above. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


119 


Slopes^  to  1 

70      80     90     1C 


20  23         30         35      40  50          GO        70      80     90    100 


FIG.  15  (Part  2  of  3). — Hydraulic  Elements  of  Trapezoidal  Sections. 


120  WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


Formulae: 

A    =   b  d  +   0.5  d2  \  Water  Surface 

P  =  b  +  2.24  d  N^1 


r-     -p 


SECTION 


Q  =  A  V 
Problem : 
b  =  50 
d  =  10.5 
V  =  4.5 

Find  r  and  Q. 

Solution: 

Enter  the  diagram  at  d  =  10.5;  thence  horizontally  to 
b  =  50  and  read  r  =  7.9.  Continuing  now  vertically  we 
note  that  the  V  =  4.5  line  is  not  intersected.  We  therefore 
divide  our  velocity  by  10  and  stop  at  V  =  0.45  and  read 
Q  =  260.  Since  this  value  of  Q  corresponds  to  a  velocity  of 
0.45,  which  is  only  one- tenth  the  velocity  given,  the  actual 
value  of  Q  is  260  X  10  =  2600. 


HYDRAULIC  DIAGRAMS   AND   TABLES 


121 


A=Area 
200          250       300     350 


Slopes  1$  to  1 

500   600  700  8009001000 


100        150      200    250   300  350  .400    500   600  700  800  9001000 

A  =Area 

FIG.  15  (Part  3  of  3). — Hydraulic  Elements  of  Trapezoidal  Sections. 


122 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


Formulae: 

P  =  b  +  2.83  d 

r  = 


b  +  2.83  d 
=  A  V 


Water  Surface 


SECTION 


Problem: 
b  =  2 
d  =  1.5 

Find  A  and  r. 

Solution  : 

Enter  the  diagram  at  d  =  1.5;  thence  horizontally  to 
6  =  2,  and  read  A  =  5.2  and  r  =  0.84. 


HYDRAULIC  DIAGRAMS   AND   TABLES 


123 


A  =  Area 


Slopes  1  to  1 


2.5          3        3.5      4 

A  =  Area 


8       9      10 


FIG.  16  (Part  1  of  3).— Hydraulic  Elements  of  Trapezoidal  Sections. 


124 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


Water  Surface 


SECTION 


Formulae: 

A  =  b  d  +  d2 
P  =  b  +  2.83  d 

A_        bd  +  d* 
~'  P  '"  b  +  2.83  d 

Q  =  A  v 

Problem : 
A  =  63 
r  =  2.75 

Find  b  and  d. 

Solution : 

Enter  the  diagram  at  A  =  63;  thence  follow  vertically 
to  r  =  2.75  (an  imaginary  line  three-fourths  of  the  distance 
from  2.6  to  2.8),  and  read  b  =  11.5  and  d  =  4.05. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


125 


10 


A  =  Area 

30        35      40 


Slopes  1  to  1 

50          GO        70      80     90   100 


25         30        35      40  50 

A  =  Area 


70      80     90   100 


FIG.  16  (Part  2  of  3).— Hydraulic  Elements  of  Trapezoidal  Sections. 


126  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Formulae: 

A    =    0  d  -\~  (L  v Water  Surface / 

P  =  b  -  2.83  d 

A        bd  +  d2  \ 1        / 


P      b  +  2.83  d 


-dr^ 


Q  =  A  V  SECTION 

Problem: 

For  an  area  of  140  square  feet  what  combination  of  bottom 
width  and  depth  gives  the  greatest  hydraulic  radius? 
Solution: 

Enter  the  diagram  at  A  =  140  and  follow  vertically  to 
the  point  indicating  the  maximum  value  of  r  which  is  when 
b  =  7  (to  the  nearest  foot)  and  d  =  8.8.  The  value  of  r 
is  4.38. 


HYDRAULIC  DIAGRAMS   AND   TABLES 


127 


100 


A  =Area  Slopes  1  to  1 

250   300   350  400    500   600  700  800  900 1000 


2000 


150 


200         250      300     350    400         500       600     700    800  900  1000 
A=Area 

FIG.  16  (Part  3  of  3). — Hydraulic  Elements  of  Trapezoidal  Sections. 


128  WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


Formulae: 

A    =   b  d  +   1.5  d2  ^  Water  Surface 

P  =  b  +  3.61  d 

~P  ''     b  +  3.61  <2 

Q  =   A    V  SECTION 

Problem: 

It  is  required  to  design  a  canal  section  to  carry  14  c.  f.  s. 
with  a  velocity  of  2.2;  the  section  to  have  a  bottom  width 
equal  to  three  times  the  depth.  Find  also  the  hydraulic 
radius. 

Solution : 

Enter  the  diagram  at  Q  =  14  and  follow  horizontally  to 
V  =  2.2;  thence  vertically  downward  to  a  point  which  indi- 
cates a  ratio  of  bottom  width  to  depth  of  3  to  1.  We  find 
this  to  be  when  b  =  3.6  and  d  =  1.2.  The  corresponding 
hydraulic  radius  r  is  found  at  the  same  time  to  be  0.82. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


129 


1 

20 

i  .' 

1. 

3 

2 

A=A 
2.5           3 

rea 

3.5       4 

5 

6 

i 

Slop 

8       J 

es 
ol 

)     10 

15 

| 

X 

:|« 

-•• 

x. 

x 

* 

* 

•' 

x  xx    x    X 

"     x'      ^ 

x 

X 

xxx 

10 
1    9 

x 

x 

. 

X 

xv 

•3 

jj|j5J  =  :j 

X 

^ 

^'^X' 

8 
7 
G 
f   5 
4 

3 
2.5 

X 

X 

X-^-^TT; 

~  1 

:^  «3 

X 

X 

X' 

• 

/ 

x 

^               ^  '    Xx 

x^ 

/ 

XXX 

^x    6° 

• 

x 

x 

X 

• 

^xxx/x/x^ 

^x'  3jj;!  -^x 

X 

? 

X 

x 

x 

x  xx^ 

x 

, 

x 

x 

xxxp/^X--^ 

x'x'x'''  X 

x" 

x 

x 

x 

2 

x 

^^x 

.  • 

X 

x 

X 

'  . 

• 

Xx  •''--'  ^^'V'' 

''''  '""'  :  x7^ 

x 

x 

X 

x 

x 

^X  ^X 

x 

•- 

? 

' 

//''/  xXXx 

x    xjx 

,x 

, 

x^ 

X 

x  ^^ 

x 

x" 

X 

-': 

•.. 

/ 

- 

''**''*'*'''''' 

'x"xx;^x 

xx 

f 

x< 

x 

x" 

x 

xx^ 

x 

x 

X 

x 

; 

>• 

/ 

", 

1 

*'''*'*''*'*'' 

^  x  "   fff^'''f  ^X^ 

x 

'xf 

x 

•XV- 

x 

x 

' 

X2   3 

x.- 

.: 

^-^A 

X' 

x 

x 

.- 

x 

x2—  z 

2 
3 

i 

j 

5---I 

"I" 

8 

fl2 

2.5 
2 

x 

X" 

x< 

X 

x     a 

X 

x^» 

7  4  a 

x' 

1 

x 

\ 

' 

3 

XV 

II 

0.9 
0.8 

0.7 
0.6 
0.5 

] 

X 

J 

^ 

x 

V 

^    ,/ 

^5  S 

^3-'  i 

x^ 

^ 

x 

^     ii 

>^V'     \ 

X 

\ 

x 

x 

>^ 

/«  ^> 

~g 

v      2 

X 

x^ 

V 

^ 

X"    / 

27 

J.v>" 

'X 

X 

/ 

^ 

^c/ 

^  8 

5 

jX        x' 

V 

^ 

/ 

X  "* 

5  9 

"j  ? 

.  '  Vj 

x/ 

x 

/^    x' 

»  ,  « 

2 

^ 

C^ 

/ 

7    . 

^^  10 

^         i' 

/''  'H<iX/ 

/ 

f 

/ 

±i! 

/ 

> 

s 

^^ 

/x       / 

Lx 

/ 

/ 

/ 

/  X 

/ 

x/ri^  xx 

'       /'      > 

S- 

L/ 

/ 

/ 

_<! 

/( 

/ 

^    .Xs 

/'       ^ 

x 

/ 

^~ 

^ 

•7 

^ 

X 

\ 

/<v-.>/    x 

/ 

x 

/ 

/ 

x 

X 

//'    /x 

'  '  I/  """'"~" 

21 

»-*^ 

x 

/ 

1 

X 

* 

/x  /'    ^ 

X 

X 

/ 

1                        1.5                 2           2.5           3        3.5      4             56789    10 
A=r  Area 

FIG.  17  (Part  1  of  3).  —  Hydraulic  Elements  of  Trapezoidal  Sections. 

130 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


SECTION 


Formulae: 

A  =  b  d  +  1.5  d* 
p  =  b  +  3.61  d 

A      bd+1.5d* 

P  ==  b  +  3.61  d 
Q  =  A  V 

Problem : 
Q  =  500 
F  =  24 
r  =  1.4 

Find  A,  b,  and  d. 

Solution: 

Neither  Q  =  500  nor  V  =  24  is  given  in  the  diagram, 
but  since  A  =  T?  we  may  divide  both  Q  and  V  by  10  before 

entering  the  diagram  and  obtain  the  required  values  of  Ay 
b,  and  d.  Enter  the  diagram  at  Q  —  50,  follow  horizontally 
to  V  =  2.4  and  read  A  =  20.8;  thence  vertically  downward 
to  r  =  1.4,  and  read  b  =  8  and  d  =  1.92. 


HYDRAULIC  DIAGRAMS  AND  TABLES 


131 


10 


A=Area  Slopes  1%  to  1 

15      20    25    30   35  40     50    60   70  80^90.100 


200 


150 


FIG.  17  (Part  2  of  3).— Hydraulic  Elements  of  Trapezoidal  Sections. 


132  WORKING   DATA  FOR  IRRIGATION   ENGINEERS 


Formulae : 

A    =    b  d  +   1.5  d2  X^  Water  Surface 

p  =  b  +  3.61  d 
A 


r  — 


P  "  b  +  3.61  d 


Q  =   A    V  SECTION 

Problem: 
b  =  60 
d  =  10.3 
7  =  3 

Find  r,  A,  andQ. 

Solution : 

Enter  the  diagram  at  d  =  10.3,  follow  horizontally  to 
b  =  60  and  read  r  =  8.0  and  A  =  780.  Following  vertically 
upward  we  note  that  V  =  3  is  not  intersected.  We,  there- 
fore, stop  at  V  =  0.3,  and  read  Q  =  235.  Since  Q  =  235 
for  V  =  0.3,  it  will  be  ten  times  235  for  V  =  3,  The  required 
value  of  Q,  therefore,  is  2350. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


133 


A = Area 
200  250       30Q>     350     400 


Slopes  1^  to  1 

500   600   700  800  900 


260   300  350  400    500   600  700  800  9001000 
A = Area 


FIG.  17  (Part  3  of  3).— Hydraulic  Elements  of  Trapezoidal  Sections. 


134  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Formulae  : 

A  =  bd  +  2d* 
P  =  b  +  4.48  d 

A_  bd+2d* 
P  ~~  b  +  4.48  d 
A  V 


~~ 


Problem :  "^  Water  Surface 

A  =  7.2                                                    ^ 
r  =  0.75  ^ T 


2(1 


Find  b  and  d.  SECTION 

Solution: 

Enter  the  diagram  at  A  —  7.2,  follow  vertically  to 
r  —  0.75  (approximately  half-way  between  r  =0.7  and 
r  =  0.8),  and  read  b  =  5  and  d  =  1.02. 


HYDRAULIC  DIAGRAMS  AND   TABLES 


135 


A  =  Area 


Slopes 

2  tol 


1.5  2  2.5 


15 


05 


3 
2.5 

2 
3 

2.5 


1.5 


0.8 


0.7 


O.G 


fe 


^X 


\ 


10 


8  rt 

A 


II 

5a 


1  1.5  2  2.5         3        3.5      4  5  6         7        8      9     10 

FIG.  18  (Part  1  of  3). — Hydraulic  Elements  of  Trapezoidal  Sections. 


136 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Formulae  : 

A  =  bd  +  2  d2 
P  =  b  +  4.48  d 


'   P        b  + 
Q  =  A  V 

Problem: 
Q  =  56 
A  =  44 
d  =  2.75 

Find  V,  b,  and  r. 
Solution  : 

Enter  the  diagram  at  Q  =  56;  follow  horizontally  to 
A  =  44  and  read  V  =  1.27;  thence  vertically  downward  to 
d  =  2.75,  and  read  b  =  10.5  and  r  =  1.93. 


SECTION 


HYDRAULIC   DIAGRAMS   AND   TABLES 


137 


200 


150 


Slopes 
2tol 

70      80    90  100 


15  20  25         30      35     40  50 

A = Area 


70      80    90  100 


(Part  2  of  3).— Hydraulic  Elements  of  Trapezoidal  Sections. 


138 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Formulae  : 

A  =  b  d  +  2  d* 
P  =  b  +  4.48  d 


= 


_ 

P  ~~ 
A  V 


Water  Surface 


SECTION 


Problem: 
A  =  640 
r  =  6.6 
Q=  1440 

Find  b,  d,  and  V. 
Solution: 

Enter  the  diagram  at  A  =  640;  follow  vertically  to  r  = 
6.6  and  read  b  =  60  and  d  =  8.4;  thence  vertically  upward 
to  Q  =  1440,  and  read  V  =  2.25. 


HYDRAULIC  DIAGRAMS  AND  TABLES 


139 


A = Area 


Slopes 
2tol 


100 


200    250   300  350  400     500   GOO   700  800  900 1000 

2000 


150      200    250   300  350  .400    500   600   700  800  900 1000 
A = Area 

FIG.  18  (Part  3  of  3). — Hydraulic  Elements  of  Trapezoidal  Sections. 


140 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


Formulae: 

A  =  bd  +  1.25  d2 
P  =  b  +  3.22  d 

A^       bd+  1.25 
=  P   =      &  +  3.22 
Q  =  A  V 


Water  Surface 


SECTION 


Fig.  19  may  also  be  used  for  canal   sections   having   both 
side  slopes  l£  to  1.    The  equations  are: 

A  =bd  +  1.25  d2 
P  =  b  +  3.20  d 

A_       bd+  1.25  d2 
~~  P   ''       6  +  3.20  d 

C  —  A  V  ' 

~  A    v  SECTION 


tt  will  be  noted  that  the  area  is  exactly  the  same  as  for  the 
mixed  slope  section  above,  but  the  wetted  perimeter,  and  con- 
sequently the  hydraulic  radius,  is  slightly  different.  The  differ- 
ence is,  however,  entirely  insignificant  for  any  practical  canal 
section. 

NOTE. — Mixed  slopes  are  seldom  used  except  for  relatively  large 
canals  on  steep  side  hills  where  steeper  slopes  are  necessary 
on  the  upper  side  to  reduce  excavation.  The  hydraulic  el- 
ements of  smaller  canals  than  those  having  a  water  area  of 
100  square  feet  have,  therefore,  not  been  plotted. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


141 


Slopes 

IK  to  1  and  1  to  1 
or 


100 


2000 


100 


150  200         250       300     350   400         500      600     700    800  9001000 

A— Area 

FlG.  19.— Hydraulic  Elements  of  Trapezoidal  Sections. 


142 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Formulae  : 

A  =  bd  +  l.75 
P  =  b  +  4.04  d 

A_  _  bd 
=  P  ~~ 
Q  =  A  V 


Water  Surface 


1.75 


b  +  4.04  d 


SECTION 


Fig.  20  may  also  be  used  for  canal  sections  having  both  side 
slopes  If  to  1.    The  equations  are: 


A  =  bd+  1.75  d2 
P  =  b  +  4.03  d 

A_   _  bd+  1.75  d2 
~~  P   ~~      &  + 4.03d2 
Q  =  A  V 


SECTION 


It  will  be  noted  that  the  area  is  exactly  the  same  as  for  the 
mixed  slope  section  above,  but  the  wetted  perimeter,  and  con- 
sequently the  hydraulic  radius,  is  slightly  different.  The  differ- 
ence is,  however,  entirely  insignificant  for  any  practical  canal 
section. 

NOTE. — Mixed  slopes  are  seldom  used  except  for  relatively  large 
canals  on  steep  side  hills  where  steeper  slopes  are  necessary 
on  the  upper  side  to  reduce  excavation.  The  hydraulic 
elements  of  smaller  canals  than  those  having  a  water  area 
of  100  square  feet  have,  therefore,  not  been  plotted. 


HYDRAULIC  DIAGRAMS  AND  TABLES 


143 


100 


Slopes 

2  to  1  and  1J£  to  1 
or 

A= Area  1%  to  1 

200          250       300     350    400          500       600     700   800    900  1000 

•712000 


1500 


150  200          250       300     350    400         500       600     700   800  9001000 

A=Area 

FIG.  20.— Hydraulic  Elements  of  Trapezoidal  Sections. 


144 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Case  I 
Segment  larger  than  semicircle. 


Formulae : 
Full  circle. 


A  =  *R* 
P  =  2?r  R 

A_ 

P   '" 


r  = 


.p. 

Case  II 
Segment  smaller  than  semicircle. 


e 


Segment.       A  =  n  R*  —  - 


P  = 


r  = 


R 


360 


90  R  sin  B 


P  2  ~0 

These  equations  apply  to  both  Case  I  and  Case  II,  provided 
the  proper  sign  is  given  to  sin  8.  For  angles  8  less  than  180 
degrees  the  second  member  of  the  equations  for  A  and  r  is 
negative  and  must  be  subtracted.  For  angles  8  greater  than 
180  degrees  the  second  member  of  the  equations  is  positive 
and  must  be  added. 

The  hydraulic  elements  of  segments  having  areas  from  0.2 
to  100  square  feet  are  given  in  Fig.  21.  For  values  not  ob- 
tainable from  the  diagram  the  table  on  the  next  page  or  the 
fundamental  equations  above  may  be  used. 

Illustrations  of  use  of  Fig.  21. 
1.  Example. — A  circular  pipe  having  a  radius  of  2  feet  has  a 

depth  of  water  of  0.95  foot.     What  are  the  area  of  water 

section  and  hydraulic  radius? 
Solution. — Enter  the  diagram  at  d  =  0.95;  follow  vertically 

to  the   intersection  with    R  =  2,  and  read  A  =  2.28  and 

r  =  0.56. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


145 


Circular  Segments 


5.0 


1.25 


.2         .25         .3     .35      .4  .5         .6       .7      .8     .9   1.0 

d  = Depth,  (feet) 


1.5  2.0        2.5 


FIG.  21  (Part  1  of  2). — Hydraulic  Elements  of  Circular  Segments. 


146 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


HYDRAULIC  ELEMENTS  OF  CIRCULAR  SEGMENTS.    ALL  VALUES  ARE  GIVEN 
IN  TERMS  OF  THE  RADIUS  R 


Depth 

Area 

Wetted  Perimeter 

Hydraulic  Radius 

0.1R 

.0588R2 

0.902R 

.0652R 

0.2R 

.  163R2 

1.285R 

.  1268R 

0.3R 

.294R2 

1.586R 

.  1852R 

0.4R 

.448R2 

1.854R 

.2415R 

0.5R 

.614R2 

2.09R 

.293R 

0.6R 

.792R2 

2.32R 

.341R 

0.7R 

.979R2 

2.53R 

.386R 

0.8R 

1.175R2 

2.74R 

.429R 

0.9R 

1.370R2 

2.94R 

.466R 

R 

1.57R2 

3.14R 

.500R 

.1R 

1.77R2 

3.34R 

.530R 

.2R 

1.965R2 

3.54R 

.555R 

.3R 

2.161R2 

3.75R 

.576R 

.4R 

2.348R2 

3.94R 

.596R 

.5R 

2.526R2 

4.19R 

.603R 

.6R 

2.692R2 

4.43R 

.608R 

1.7R 

2.846R2 

4.69R 

.607R 

1.8R 

2.977R2 

5.00R 

.595R 

1.9R 

3.081R2 

5.38R 

.565R 

2R 

3.142R2 

6.28R 

.500R 

NOTE. — This  table  is  intended  for  use  in  calculating  the  hydraulic  elements  of  circu- 
lar segments  having  an  area  greater  than  100  square  feet,  which  is  the  limit  of  the  diagram. 
It  has,  however,  general  application  and  may  be  used  for  calculating  any  circular  segment. 

2.  Example. — What  are  the  hydraulic  radius  and  depth  of  flow 
of  a  pipe  of  6  feet  radius  when  the  area  is  75  square  feet? 

Solution. — Enter  the  diagram  at  A  =  75;  follow  horizontally 
to  the  line  representing  R  =  6,  and  read  d  =  7.55  and 
r  =  3.4. 

3.  Example. — For  an  area  of  25  square  feet  what  radius  of 
pipe  will  give  the  greatest  hydraulic  radius? 

Solution. — Enter  the  diagram  at  A  =  25;  follow  horizontally 
to  the  point  indicating  the  greatest  hydraulic  radius,  which 
is  when  R  =  4  feet. 

4.  Example. — The  area  of  a  segment  is  30  square  feet  and  the 
depth  of  flow  is  4  feet.    What  are  the  radius  of  segment  and 
hydraulic  radius? 

Solution. — Enter  the  diagram  at  A  =  30;  follow  horizontally 
to  the  vertical  line  representing  d  =  4,  and  read  by  inter- 
polation R  =  5.8,  also  r  =  2.15. 


HYDRAULIC  DIAGRAMS  AND   TABLES 


147 


Circular  Segments 

8     7 


1.5  2.0  2.5        3.0      3.5     4.0          5.0        6.0      7.0     8.0    9.0  10.0- 

d=Depth  (feet) 
FIG.  21  (Part  2  of  2). — Hydraulic  Elements  of  Circular  Segments. 


148  WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


Horseshoe  Sections 

Sections  having  the  upper  portion  in  the  form  of  a  semicircle 
and  the  lower  portion  composed  of  arcs  of  larger  radius,  or  of 
straight  lines,  are  commonly  called  " horseshoe "  sections.  They 
are  frequently  used  for  tunnels  in  yielding  material  and  for 
outlet  conduits  under  earth  dams. 

The  horseshoe  section  has  some  hydraulic  and  structural 
advantages  over  circular  and  other  sections.  The  hydraulic 
value  of  the  section  illustrated  on  the  opposite  page,  for  a  depth 
of  flow  of  1.6  R  (or  clearance  C  =  0.4  R),  may  be  seen  by  com- 
paring the  area  and  hydraulic  radius  of  this  section  for  this 
condition  with  the  same  elements  for  a  circular  section  as  given 
in  the  table  on  page  146.  The  areas  are  seen  to  be  2.85  R2  and 
2.692  R2  respectively,  and  the  hydraulic  radii  0.610  R  and 
0.608  R  respectively.  Structurally  the  horseshoe  section  affords 
more  floor  room  and  permits  the  building  of  the  sides  and  arch 
of  the  lining  before  the  invert  is  put  in — important  factors  in 
tunnel  work. 

It  is  said  that  the  most  favorable  section  of  the  horseshoe 
type  is  when  the  total  height  is  equal  to  the  greatest  width,  as  in 
the  section  illustrated  on  page  149.  The  calculation  of  the 
hydraulic  elements  of  such  sections  is  a  tedious  process  and  much 
labor  may  be  saved  by  the  use  of  the  table  on  the  opposite  page. 
Slight  deviations  from  the  given  section,  such  as  making  the 
sides  below  the  center  line  straight  and  the  bottom  of  two 
straight  lines,  will  still  allow  the  use  of  this  table  for  preliminary 
calculations  on  which  to  base  the  size  of  the  section.  After  the 
size  and  form  have  been  decided  upon,  more  exact  calculations 
of  the  hydraulic  elements  can  be  made  if  desired. 


HYDRAULIC  DIAGRAMS  AND   TABLES 


149 


HYDRAULIC  ELEMENTS  OF  A  HORSESHOE  SECTION 


All  values  are  given  in  terms  of  R 


Clearance  C 

Area 

Wetted  Perimeter 

Hydraulic  Radius 

0 

3.30R2 

6.52R 

0.506R 

0.1R 

3.24R2 

5.62R 

0.576R 

0.2R 

3.13R2 

5.24R 

0.598R 

0.3R 

3.01R2 

4.93R 

0.610R 

0.4R 

2.85R2 

4.67R 

0.610R 

0.5R 

2.69R2 

4.43R 

0.607R 

0.6R 

2.51R2 

4.18R 

0.600R 

0.7R 

2.32R2 

3.99R 

0.582R 

0.8R 

2.12R2 

3.78R 

0.561R 

0.9R 

1.93R2 

3.58R 

0.539R 

R 

1  .  73R2 

3.38R 

0.512R 

Example  1. — The  section  has  a  radius  R  of  5  feet.  The  surface 
of  the  water  is  one  foot  below  the  top.  What  are  the  area 
and  hydraulic  radius? 

Clearance  C  =  1/5  R  =  0.2  R 

Area  =  3.13  R2  =  78.2  sq.  ft. 
Hydraulic  radius  =  .598  R  =  2.99  feet 

Example  2. — The  required  area  of  water  section  is  125  square 
feet  and  the  clearance  of  water  surface  below  top  shall  be 
0.3  R.  What  is  the  radius? 

Area  =  3.01  R2  =  125 
.'.  R  =  6.45  feet 
Hydraulic  radius  =  0.61  R  =  3.93  feet 

Clearance  C  =  6.45  X  0.3  =  1.94  feet 


150 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  22 
CIRCULAR  CONDUITS  FLOWING  PARTLY  FULL 

(Kutter  Formula) 

Values  by  which  discharge  and  velocity  of  a  circular  conduit  flowing  full 
should  be  multiplied  to  obtain  the  discharge  and  velocity  of  the  same  conduit 
with  the  proportionate  depth  on  invert  given  in  the  first  column.  For  use 
with  Fig.  22.  D  =  diameter  of  conduit. 

Depth  of  flow 


Proportionate  depth 


D 


i  flj  —  . 

D  = 

1  FT. 

D  = 

2  FT. 

D  = 

4  FT. 

D  = 

6  FT. 

D  =  ] 

OFT. 

11! 

<vsQ 

Velo- 
city 

Dis- 
charge 

V 

Q 

V 

Q 

V 

Q 

V 

Q 

.10 

.333 

.0174 

.351 

.0183 

.370 

.0193 

.379 

.0198 

.388 

.0202 

.11 

.359 

.0216 

.377 

.0226 

.396 

.0237 

.405 

.0242 

.414 

.0247 

.12 

.385 

.0262 

.403 

.0274 

.421 

.0286 

.430 

.0292 

.438 

.0298 

.13 

.410 

.0313 

.428 

.0327 

.446 

.0340 

.454 

.0346 

.461 

.0352 

.14 

.433 

.0369 

.452 

.0385 

.469 

.0399 

.477 

.0406 

.484 

.0412 

.15 

.456 

.0429 

.475 

.0447 

.492 

.0463 

.500 

.0470 

.507 

.0477 

.16 

.478 

.0494 

.497 

.0513 

.514 

.0531 

.522 

.0539 

.529 

.0547 

.17 

.501 

.0564 

.518 

.0583 

.535 

.0604 

.544 

.0613 

.551 

.0621 

.18 

.523 

.0640 

.539 

.0660 

.557 

.0682 

.565 

.0691 

.572 

.0700 

.19 

.544 

.0720 

.560 

.0742 

.578 

.0764 

.586 

.0775 

.592 

.0784 

.20 

.565 

.0804 

.581 

.0827 

.598 

.0851 

.606 

.0863 

.612 

.0871 

.21 

.585 

.0892 

.601 

.0916 

.617 

.0942  \ 

.625 

.0955 

.631 

.0963 

.22 

.604 

.0985 

.620 

.101 

.635 

.104 

.643 

.105 

.649 

.106 

.23 

.623 

.108 

.638 

.111 

.653 

.114 

.660 

.115 

.666 

.116 

.24 

.642 

.118 

.656 

.121 

.670 

.124 

.677 

.126 

.683 

.126 

.25 

.660 

.129 

.674 

.132 

.687 

.134 

.694 

.136 

.700 

.137 

.26 

.677 

.140 

.691 

.143 

.704 

.145 

.711 

.147 

.716 

.148 

.27 

.695 

.152 

.708 

.154 

.720 

.157 

.727 

.159 

.732 

.159 

.28 

.713 

.164 

.725 

.166 

.736 

.169 

.743 

.171 

.748 

.171 

.29 

.729 

.176 

.741 

.178 

.752 

.181 

.758 

.183 

.763 

.183 

.30 

.745 

.188 

.756 

.191 

.768 

.194 

.773 

.195 

.778 

.196 

.31 

.760 

.201 

.771 

.204 

.782 

.207 

.787 

.208 

.792 

.209 

.32 

.776 

.214 

.785 

.217 

.796 

.220 

.801 

.221 

.806 

.222 

.33 

.791 

.228 

.800 

.231 

.810 

.233 

.815 

.234 

.819 

.235 

.34 

.806 

.242 

.815 

.245  • 

.824 

.247 

.828 

.248 

.832 

.249 

.35 

.821 

.257 

.830 

.259 

.837 

.261 

.841 

.262 

.844 

.263 

.36 

.835 

.271 

.843 

.274 

.850 

.275 

.854 

.276 

.857 

.277 

.37 

.848 

.286 

.856 

.289 

.863 

.290 

.866 

.291 

.869 

.292 

.38 

.862 

.301 

.869 

.304 

.875 

.305 

.878 

.306 

.881 

.307 

.39 

.875 

.316 

.882 

.319 

.887 

.320 

.890 

.321 

.893 

.322 

.40 

.888 

.332 

.894 

.334 

.899 

.336 

.901 

.337 

.905 

.338 

.41 

.900 

.348 

.906 

.349 

.910 

.351 

.912 

.352 

.916 

.353 

.42 

.912 

.364 

.917 

.365 

.921 

.367 

.923 

.368 

.927 

.369 

.43 

.924 

.380 

.929 

.381 

.932 

.383 

.934 

.384 

.936 

.385 

.44 

.936 

.397 

.940 

.398 

.943 

.399 

.944 

.400 

.945 

.401 

.45 

.948 

.414 

.951 

.415 

.953 

.416 

.954 

.416 

.955 

.417 

.46 

.960 

.431 

.961 

.432 

.963 

.433 

.964 

.433 

.965 

.434 

.47 

.970 

.448 

.971 

.449 

.973 

.450 

.973 

.450 

.974 

.451 

.48 

.980 

.465 

.981 

.466 

.982 

.466 

.982 

.466 

.983 

.467 

.49 

.990 

.482 

.991 

.483 

.991 

.483 

.991 

.483 

.992 

.483 

.50 

1.000 

.500 

.000 

.500 

1.000 

.500 

.000 

.500 

1.000 

.500 

.51 

1.009 

.517 

.009 

.517 

1.009 

.517 

.009 

.517 

.008 

.517 

.52 

1.018 

.535 

.018 

.534 

1.017 

.534 

.017 

.534 

.016 

.533 

.53 

1.027 

.553 

.026 

.552 

1.025 

.551 

.025 

.551 

.023 

.550 

.54 

1.036 

.571 

.035 

.570 

1.033 

.568 

.033 

.568 

.030 

.567 

.55 

1.045 

.589 

1.043 

.588 

1.040 

.586 

1.040 

.586 

.037 

.584 

HYDRAULIC   DIAGRAMS   AND    TABLES 


151 


f 

25      Multipl  era  for  other  

2          s 

2 

or 

Circular  Conduits? 

d          c^i         ?! 

M£ 

20        ?• 

4 
0 
!=          10 

,ues  of  "n" 

^".^".016 
1.107    .010  -826 
1.100  .910  .839 
1.095    .922  .80! 
1.090    .025  .856 
1.086    .928  .862 

/ 

'v 

TMHI  / 

N- 

2G 
28 
30 

33 

1 
1 

/^ 

H^ 

/ 

t^ 

,           s 

/                /x^ 

/ 

X, 

x 

^ 

s 

f 

<  / 

/ 

X 

I 

/ 

N  ^          ' 

/S, 

/ 

k  o 

x 

" 

/    XJn            ' 

1 

1 

x 

s 

*v 

1  / 

S/ 

^-x/ 

, 

x 

f 

N 

J  '  ^ 

/          7s 

y 

\^ 

1 

y 

/ 

-i     / 

y 

y1 

S^ 

/ 

'x 

/ 

. 

s* 

>     7 

1    Vk    ' 

2 

10     -+-  -  -  - 

1 

x^ 

5 

1 

2 

1 

2s   _L 

/  s\. 

I 

2 

! 

r 

N  ./ 

X 

A, 

t 

v                / 

7 

/x^ 

/* 

v 

y 

s 

J 

/ 

y 

7 

[  j  j       / 

1 

j 

x^ 

y 

5?! 

A, 

/         '  -.1 

y 

^ 

L    y( 

y 

/ 

i 

'x  ^  y 

i  "\ 

' 

/ 

^ 

1 

s 

To' 

/ 

/v    / 

f       7 

Q     . 

f^^ 

1 

\ 

S 

Q 

y 

,          N{ 

i       1 

S 

j         \ 

/ 

\ 

y 

1 

1 

x 

>x 

/ 

r            r 

•  "  '      / 

/ 

\^ 

/ 

^ 

x 

x 

/ 

7 

! 

/ 

1 

\ 

/ 

^ 

I 

^ 

5; 

/ 

TJX 

f 

/  Nx, 

7 

1-1    i   ™ 

Xl      / 

^y 

/ 

^ 

I 

/ 

\ 

[ 

y 

^»        ^ 

y                 y 

N 

R   1 

|VN 

/ 

x 

x 

y 

'/ 

\i 

sy 

, 

* 

7        ^^>. 

/    / 

~S2-5  |::: 

1 

I 

1 

ft 

A 

s 

^ 

4 

/s 

s 
i 

n 

.2      ;j?:: 

"3          -;''•;•• 
e8            /--kt 

-  —  -£ 

-^ 

-/- 

^ 

7^ 

?/ 

j| 

s^ 

-f 

y^ 

^ 

/ 

_  j     2 

::!(!  ~^ 

/ 

,2 

/ 

1 

42  a 

45 
43 
51 
54 

57 

£1.5    £--•• 

,,.J 

—j 

y1 

^ 

^ 

7 

. 

7  " 

I 

? 

e; 
1 

! 

7" 

/ 

"I*" 

<7 

H 

/ 

^ 

^ 

1 

1 

w                       / 

/ 

1 

y 

y 

V 

~v/ 

T 

i 

V      / 

/ 

/ 

x 

/ 

y 

y 

0 

i     \/ 

' 

"7 

"*x/ 

y* 

/ 

j 

» 

,  / 

c/7 

A        ' 
'^*t. 

/        / 

N  t 

~7 

~~r 

x,.^ 

A 

s*V 

s 

i            "/ 

r- 

f 

/ 

v' 

s  / 

i 

/  fs 

y 

£ 

V                 / 

r 

9     --/-- 

^  s 

1 

^^ 

/•* 

/- 

7 

N 

j 

/ 

^  / 

vi'        X 

E_V 

/ 

y 

A 

y 

i 

r         ^ 

Sv  /I 

7     i 

y 

X1 

^ 

! 

i 

N 

^  '          /N      / 

A                   / 

y 

y 

y 

^ 

y 

y 

y 

f  "  r  2. 

^    -(  / 

^ 

/ 

/    X   / 

f 

y1 

y 

yk 

y 

y 

f 

j  j 

/      XS/ 

/v 

1 

f 

; 

y1 

y                 ^ 

>  ••'•  r^§ 

5    --/-  - 

f 

'S 

1 

/ 

7 

/ 

s 

^ 

y             / 

/  •    / 

/ 

t 

7 

V 

7 

^ 

/ 

/ 

7 

s 

N 

1 

/           ^ 

'   y 

7 

.4    /-—  - 

/_ 

/ 

/s 

x1 

(/ 

x 

/ 

/ 

/ 

^ 

r     /^ 

f                         I                     y 

_x 

/        / 

/ 

/ 

^ 

/ 

/ 

J 

1 

S  >        / 

!'  j7 

/ 

3          ^ 

/ 

/ 

/ 

/ 

t 

/ 

> 

/ 

/ 

/ 

//   !! 

'«=H 

/ 

.25  -::: 

::|:- 

/- 

y 

/ 

V 

- 

y 

/IKI 

2.5       3  4          5        6       7     8     9  10  15  20         25      30  40 

Discharge  in  Cubic  Feet  per  Second 

FIG.  22  (Part  1  of  2). — Discharge  of  Circular  Conduits  Flowing  Full 
by  Kutter  Formula. 

(Explanation  page  78.) 


152 


WORKING   DATA  FOR   IRRIGATION   ENGINEERS 


TABLE   22  (Concluded} 
CIRCULAR  CONDUITS  FLOWING  PARTLY  FULL 


si  fli 

<D  = 

LFT. 

D  = 

2  FT. 

D  = 

4  FT. 

D  = 

6  FT. 

D  =  1 

0  FT. 

HI 

ill 

Velo- 
city 

Dis- 
charge 

V 

Q 

V 

Q 

V 

Q 

V 

Q 

.56 

1.053 

.607 

1.051 

.606 

1.047 

.604 

1.047 

.603 

1.044 

.602 

.57 

1.061 

.625 

1.058 

.624 

1.054 

.622 

1.054 

.620 

1.051 

.619 

.58 

1.069 

.643 

1.065 

.642 

1.061 

.639 

1.060 

.637 

1.057 

.636 

.59 

1.076 

.660 

1.072 

.659 

1.068 

.656 

1.068 

.654 

1.063 

.653 

.60 

1.083 

.678 

1.078 

.676 

1.074 

.673 

1.072 

.671 

1.069 

.670 

.61 

1.089 

.696 

1.084 

.694 

1.080 

.690 

1.078 

.689 

1.075 

.687 

.62 

1.095 

.714 

1.090 

.711 

1.086 

.707 

1.084 

.706 

1.081 

.704 

.63 

1.101 

.732 

1.096 

.728 

1.092 

.724 

1.090 

.723 

1.087 

.721 

.64 

1.107 

.749 

1.102 

.745 

1.097 

."741 

1.095 

.740 

1.092 

.738 

.65 

1.113 

.766 

1.107 

.762 

1.102 

.758 

1.100 

.757 

1.097 

.755 

.66 

1.117 

,783 

1.112 

.779 

1.107 

.775 

1.105 

.773 

1.101 

.771 

.67 

1.123 

.800 

1.117 

.796 

1.111 

.791 

1.109 

.789 

1.105 

.787 

.68 

1.129 

.817 

1.122 

.813 

1.115 

.807 

1.113 

.805 

1.109 

.803 

.69 

1.133 

.834 

1.126 

.829 

1.119 

.823 

1.116 

.821 

1.113 

.819 

.70 

1.137 

.851 

1.130 

.845 

1.122 

.839 

1.119 

.837 

1.117 

.835 

.71 

1.141 

.867 

1.134 

.860 

1.126 

.854 

1.123 

.852 

1.120 

.850 

.72 

1.145 

.883 

1.137 

.875 

1.129 

.869 

1.126 

.867 

1.123 

.865 

.73 

1.148 

.898 

1.140 

.890 

1.132 

.884 

1.129 

.882 

1.125 

.880 

.74 

1.150 

.913 

1.142 

.905 

1.134 

.899 

1.131 

.897 

1.127 

.894 

.75 

1.152 

.928 

1.144 

.920 

1.136 

.914 

1.133 

.911 

1.129 

.908 

.76 

1.154 

.942 

1.146 

.934 

1.138 

.928 

1.135 

.925 

1.131 

.922 

.77 

1.156 

.956 

1.148 

.948 

1.140 

.942 

1.136 

.939 

1.133 

.936 

.78 

1.157 

.969 

1.149 

.962 

1.141 

.955 

1.137 

.952 

1.134 

.949 

.79 

1.159 

.982 

1.150 

.975 

1.142 

.968 

1.138 

.965 

1.135 

.962 

.80 

1.160 

.994 

1.151 

.987 

1.143 

.980 

1.139 

.977 

1.136 

.974 

.81 

1.161 

1.006 

1.152 

.999 

1.144 

.992 

1.140 

.989 

1.137 

.972 

.82 

1.161 

1.017 

1.152 

1.010 

1.144 

.004 

1.140 

1.000 

1.137 

.996 

.83 

1.160 

1.028 

1.151 

1.021 

1.143 

.015 

1.139 

1.011 

1.136 

1.007 

.84 

1.159 

1.038 

1.150 

1.031 

1.142 

.025 

1.138 

1.021 

1.135 

1.017 

.85 

1.157 

1.048 

1.148 

1.041 

.141 

.034 

1.137 

1.030 

1.134 

1.027 

.86 

1.155 

1.057 

1.146 

1.050 

.139 

.042 

1.135 

1.038 

1.132 

1.035 

.87 

1.152 

1.065 

1.144 

1.058 

.137 

.050 

1.133 

1.046 

1.130 

1.043 

.88 

1.149 

1.071 

1.141 

1.064 

.134 

.057 

1.130 

1.053 

1.127 

1.050 

.89 

1.146 

1.077 

1.138 

1.070 

.131 

.063 

1.127 

1.059 

1.124 

1.057 

.90 

1.142 

1.082 

1.134 

1.075 

.127 

.068 

1.123 

1.065 

1.121 

1.063 

.91 

1.137 

1.086 

1.130 

1.079 

.123 

.072 

1.119 

1.069 

1.117 

1.067 

.92 

1.132 

1.090 

1.125 

1.083 

.118 

.076 

1.114 

1.072 

1.112 

1.070 

.93 

1.125 

1.091 

1.119 

1.085 

.112 

1.078 

1.109 

1.075 

1.107 

1.073 

.94 

1.118 

1.091 

1.112 

1.085 

1.105 

1.078 

1.102 

1.075 

1.100 

1.073 

.95 

1.109 

1.088 

1.103 

1.082 

1.097 

1.076 

1.095 

1.074 

1.093 

1.072 

1.00 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

NOTE. — For  any  diameter  greater  than  10  feet  that  is  likely  to  be  used  in  practice  the  multi- 
pliers are  practically  the  same  as  for  the  10  feet  diameter. 

There  is 'a  slight  variation  with  the  slope  that  is  not  accounted  for  in  the  above  table.  For 
slopes  greater  than  .0005  the  error  of  the  table  from  this  source  is  usually  less  than  one  per  cent. 
For  flatter  slopes  the  error  is  somewhat  greater. 

This  table  is  adapted  from  tables  in  Garrett's  "  Hydraulic  Diagrams  for  Practical 
Engineers." 


HYDRAULIC   DIAGRAMS   AND   TABLES 


153 


25 

8 

X/~ 

C* 

O1 

\ 

? 

i 

! 

g 

q     * 

S     S    Z 

15 

Circular  Conduits 
W=.013 

§        §        ^ 

20 
15 

10 
9 

8 
7 
6 

5 

I4 

0 
£3.0 

02.5 

s 

s- 

/ 

LV 

! 

%! 

rln/nin 

:i:h;|S 

7 

j 

E 

/ 

7 

/s 
84 

90 
9G 
102 
108 
114 

vo 

X 

/ 

/ 

*  ^ 

^y 

^  /  ^  •  ^ 

1  s      /    >N/ 

"^t 

1< 

^ 

X. 

/ 

1 

x 

1 

/ 

\ 

J        ^  x 

/    Xyi        5^x, 

/    j 

^ 

•^ 

^ 

/ 

N 

1 

V 

I—  *        Z      s 

7          /    >  ( 

^j™ 

N 

V 

\ 

^ 

\ 

/ 

x^ 

\    ,         V 

f  X  .         j  Xw  / 

s 

/ 

x^ 

1 

X. 

/ 

> 

"SJ 

7 

\ 

j 

X        j                    ^s, 

^^ 

x/ 

X 

! 

x 

/ 

X^ 

^ 

^ 

j     2  j 

**•  1    J!:2 

x 

1 

X^ 

^ 

x 

( 

x^ 

y 

I 

K 

/ 

* 

,y 

x^ 

f 

^                       s 

'    s  /       /V 

\ 

/s 

N 

j 

/ 

/ 

x 

•^, 

2,       L    N 

v    ]    »  J 

v 

X^ 

"s 

y. 

X 

/ 

x 

x 

f 

X 

/ 

' 

^ 

1     ^      / 

>Ss       /     ^JS^ 

/ 

X^ 

/ 

X 

s/ 

X 

7 

X 

s  ^ 

N 

y 

"^x 

V 

^  X       /         Xs 

/      ?"«,•     t 

/XN 

1 

N, 

N 

1 

x 

/ 

V 

x/ 

/ 

X 

1 

2 

sJ 

N 

r    2"x,z 

'      *  \                ^[X 

f 

s-> 

/ 

x 

•^ 

y 

^ 

X       r          >          7 

-  -  ft      / 

x^ 

^x^ 

/ 

Nj 

V        / 

/ 

s 

1 

^ 

X 

^ 

^ 

^          L 

x    /            Z 

7 

\ 

/ 

x 

I 

•^ 

^ 

f-  4 

i^ 

^^ 

^  X  J        ^ 

5:3         \ 

/ 

x 

-/* 

A 

' 

I 

X 

y 

1 

Xi 

y1 

/ 

^ 

y           f   ***>  J 

>         .  / 

v, 

y*X" 

X 

j 

1 

/x 

^ 

s 

1 

£   7   ]IiJ 

^ 

/    ' 

X  / 

^ 

s 

x 

x/ 

/ 

^ 

y 

X, 

/ 

/ 

^  Z 

Y/       ^         "V 

/" 

^ 

/ 

•x^ 

/ 

/x 

s 

/ 

/ 

x 

v 

^/ 

/x 

j 

'  2  " 

VCV         / 

x 

1 

^ 

x 

x 

^ 

V 

X 

7 

x 

s. 

^ 

/ 

\ 

/     /      ?  ^  5s 

v^ 

/ 

^  v 

s/ 

^< 

r 

7 

N 

/ 

s^ 

7 

/ 

^ 

J 

/ 

^x     Z 

')'"        /       N 

2 

/   ^ 

V 

/ 

^ 

X    / 

/ 

^ 

s 

/ 

^s 

t 

r    ^xf 

/        **t           < 

^ 

x^ 

^ 

^ 

£ 

X 

1 

/ 

f 

x 

/ 

/ 

^ 

^ 

77      >^ 
-  >•  -       t 

'*!  ^   / 

x  / 

^ 

x 

/ 

f 

s 

y    X 

I/ 

& 

^- 

3 

^x 

i 

\ 

i 

-) 

i  „  / 

r 

V 

-/ 

I 

\ 

x 

( 

0 

3 
t1'5 

1.0 
.9 
.8 

.7 
.6 

.5 

.4 

.3 

.25 

4 

F 

x/ 

-/ 

x 

> 

X/ 

y 

~s 

7 

ft 

I 

4 

S7 

7' 

fx- 

_j          7 

V;--  -^  -y 

^- 

2 

^X 

^ 

s 

^ 

A 

132 
144 

7~ 

x 

/x 

1 

.  i 

^    7         > 

/*    X     / 

/ 

'  N 

y 

^ 

/ 

x 

/ 

x 

y 

i 

^ 

/ 

/ 

if. 

/ 

2  >•  ^}  £         L 

,                >X. 

/ 

/ 

^  / 

1 

/x 

1 

y 

/ 

*3 

*h   ^  -  1 

x 

1 

i 

/  N 

.y 

N 

1 

I 

^ 

y 

S       ®^C  "  s 

^         /'       / 

^> 

i 

/ 

/ 

x 

\ 

1 

^ 

/ 

/ 

\ 

"y      l|  f  W 

^x    /      / 

/ 

x 

^ 

/ 

/ 

N 

x 

/ 

f 

\ 

/ 

/ 

f 

^ 

^ 

I 

x. 

ss 

/      <5s  '  /    4/ 

?VK  / 

7 

/ 

^ 

\ 

/ 

/ 

1 

/x 

t 

/ 

V 

i 

5k  Z  -!' 

^  /    '  x^ 

/ 

1 

^ 

^ 

X 

1 

/ 

f 

x 

f 

/ 

x/ 

^ 

^              ^ 

A.V            '        "V 

/ 

f 

V 

x  > 

y 

f* 

/ 

/ 

X 

/  ^        , 

^/          / 

\/ 

f 

/ 

X 

\ 

/ 

> 

V 

•/            s 

/  '  F? 

/ 

x/ 

/ 

N 

-f 

j(- 

~1 

— 

x^--/-  -i 

/7^ 

/— 

•^ 

— 

1 

1 

•J 

1 

y 

X 

y 

7       ^x7 

x      /         / 

0,'V 

^ 

y 

/ 

/ 

•y 

/ 

>X 

H 

_y        ^.    1 

^          ^.    / 

/ 

3 

I 

\ 

v, 

/ 

/ 

<*, 

/ 

y. 

'      Z  '  * 

^     '   7^ 

/ 

/ 

s/ 

/ 

/ 

^ 

/ 

1 

X 

/ 

/ 

^•7    7 

>                 / 

\y 

/ 

( 

/ 

/- 

X 

/ 

v,^ 

1 

y          ^S                   ' 

i      I'    / 

/ 

X 

/ 

"** 

/ 

/ 

% 

j 

/ 

y. 

/                  '          *    > 
t               1       S, 

/    ^  7^> 

7 

A 

'x 

/ 

/ 

7 

/ 

, 

' 

N 

/ 

• 

/ 

^ 

N         '            j 

?       /      / 

x> 

x/ 

/ 

; 

X 

/ 

y 

) 

^ 

^, 

/ 

1 

^  ^'Z 

/ 

x 

/ 

/ 

/ 

* 

X. 

/ 

/ 

/ 

N 

y 

/ 

Z       K 

(.ill 

V 

/ 

_ll    

0         50      GO    70    80  90  100                150          200      250     300     •     400       500 

Discharge  in  Cubic  Feet  per  Second 
IG.  22  (Part  2  of  2).  —  Discharge  of  Circular  Conduits  Flc 

600 

>win 

700800 

gFull 

by  Kutter  Formula. 


154  WORKING   DATA  FOR  IRRIGATION   ENGINEERS 


Small 
Wooden-Flumes 


/> 


s 

II 


§    i    i.    i   i.    i    i.    i   i    § 

00<=>0<=>0|=>0<=><=) 


FIG.  23  (Part  1  of  3).  —  Discharge  of  Rectangular  Wooden  Flumes. 
(Explanation  page  80.) 


HYDRAULIC   DIAGRAMS   AND   TABLES 


155 


Small 
Wooden  Flumes 


FIG.  23  (Part  2  of  3).— Discharge  of  Rectangular  Wooden  Flumes. 


156 


WORKING  DATA  FOR  IRRIGATION  '  ENGINEERS 


Small 
Wooden  Flumes 


S3 


-v/ 


3 

B  o^o 

s     M 

o     -  * 
fc     ^ 


\ 


^  8, 


o  o 


o  o* 


FIG.  23  (Part  3  of  3).— Discharge  of  Rectangular  Wooden  Flumes. 


HYDRAULIC  DIAGRAMS  AND  TABLES 


157 


Small 
Wooden  Flumes 


FIG.  24  (Part  1  of  3). — Discharge  of  Rectangular  Wooden  Flumes. 
(Explanation  page  80.) 


158 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Small 
Wooden  Flumes 


3  2 
3  s 


S.2 
5 

s 


Vi 


-\ 


FIG.  24  (Part  2  of  3). — Discharge  of  Rectangular  Wooden  Flumes. 


HYDRAULIC  DIAGRAMS  AND  TABLES 


159 


Small 
Wooden  Flumes 


is. 


1 


adois 
FIG.  24  (Part  3  of  3). — Discharge  of  Rectangular  Wooden  Flumes. 


160 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


puooog  aad  ^88 j 
FIG.  25. — Hydraulic  Curves  for  Small  Canals. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


161 


x^- 

' 

X-- 

^x 

? 

^^ 

-^ 

x 

x 

^x 

^ 

>- 

-** 

b 

x 

^, 

5 

^  - 

,  — 

^ 

Y> 

/ 

- 

-^ 

^^> 

-^ 

/ 

& 

2 

2* 

^ 

•^ 

~? 

\ 

^y 

>- 

-^^"^ 

/ 

/ 

1 

c 

!sL 

^ 

/ 

x 

/ 

/ 

' 

s 

r 

/ 

t 

/ 

^ 

s 

s 

de 

SI 

op 

ss 

l^ 

to 

1 

/ 

/ 

/ 

/ 

^ 

'  / 

/ 

// 

V 

t 

// 

7) 

~& 

I' 

)                        10                       20                       30                       40                        50                       6( 

Area  of  Water  Section 
FIG.  25J^. — Curves  for  Proportioning  the  Section. 

I 

Use  of  Figs.  25  to  28 
1.  Problem: 

What  slope  of  water  surface  is  required  for  a  canal  to 
have  a  discharge  of  60  c.  f.  s.,  a  mean  velocity  of  2.2  feet  per 
second,  lJ/2  to  1  side  slopes,  and  a  ratio  of  bottom  width  to 
depth  of  2  to  1?  n  =  .0225.  Also  find  the  required  bottom 
width  and  depth. 

Solution: 

In  Fig.  25,  at  the  intersection  of  the  lines  representing 
Q  =  60  and  V  =  2.2  we  read  S  =  .00058.  At  the  same 
time  we  read  on  the  diagonal  line  the  area  of  water  section 
equals  27.  To  find  the  required  bottom  width  and  depth  we 
now  turn  to  Fig.  25j^  and  at  the  intersection  with  the  im- 
aginary line  representing  area  =  27  and  the  line  marked 
"b  =  2d"  we  read  d  =  2.7  +;  and  b  is  therefore  equal  to 
2.7  X2or  5.4  feet. 

The  hydraulic  elements  of  the  canal  section  then  are: 

Q  =  60  [     b  =  5.4 

V  =  2.2  d  =  2.7 

5  =  .00058          n  =  .0225 
Side  slopes  lj^  to  1 


162  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

If  the  canal  were  to  have  a  ratio  of  bottom  width  to  depth 
of  3,  Fig.  25  would  be  used  in  the  same  manner  as  above,  but 
in  using  Fig.  25  J^  the  line  marked  "b  =  3d"  would  be  used 
and  we  would  find  d  =  2.45  and  b  =  2.45  X  3  =  7.35.  The  line 
marked  "  b  =  d"  is  used  in  a  similar  manner  to  proportion  a 
section  having  this  ratio.  The  other  elements  of  the  canal 
section  would  remain  as  above.  The  results  in  the  latter 
cases  would  not  be  exact  because  Fig.  25  is  based  on  a  ratio 
of  bottom  width  to  depth  of  2  to  1,  but  the  error  is  not  of 
practical  significance  for  canals  of  the  sizes  considered. 

For  n  =  .025,  Fig.  26,  instead  of  Fig.  25,  is  used,  but 
Fig.  25}/2  is  used  in  the  same  manner  as  above  outlined. 


2.  Problem: 

What  slope,  bottom  width,  and  depth  are  required  for  a 
canal  to  carry  5  c.  f.  s.  if  the  velocity  is  to  be  1.5  feet  per 
second,  side  slopes  1^  to  1,  ratio  of  bottom  width  to  depth 
2  to  1,  and  n  =  .025? 

Solution: 

In  Fig.  28,  at  the  intersection  of  the  lines  representing 
Q  =  5,  and  V  =  1.5,  we  read  S  =  .0016,  and  interpolating 
between  diagonal  lines  we  find  the  area  of  water  section  to 
be  3.3  square  feet.  Turning  now  to  Fig.  27J^,  we  read  at  the 
intersection  of  the  imaginary  line  representing  area  =3.3 
with  the  line  marked  "b  =  3d"  that  d  =  0.85  foot;  hence 
b  =  3  X  0.85  =  2.55  feet. 

The  hydraulic  elements  of  the  canal  section  then  are  : 

Q  =  5 

V=  1.5 

S  =  .0016 

b  =  2.55 

d  =  0.85 

n  =  .025 

Side  slopes  lj^  to  1 


HYDRAULIC   DIAGRAMS   AND   TABLES 


163 


puooag  J9d  ^89,1  UT 
FIG.  26. — Hydraulic  Curves  for  Small  Canals. 


164  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


1.5 


1.0 


Bide  Slopes  1^  to  1 


234 
Area  of  Water  Section 


FIG.  27^. — Curves  for  Proportioning  the  Section. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


165 


Area  Square  Feet 


1.0  1.5  2.0 

Velocity  in  Feet  per  Second 


2.5 


FIG.  27.  —  Hydraulic  Curves  for  Small  Laterals. 


3.0 


Area  Square  Feet 


1.0  1.5  2.0 

Velocity  in  Feet  per  Second 

FIG.  28. — Hydraulic  Curves  for  Small  Laterals. 


3.0 


166 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  23 

SEMICIRCULAR  STEEL  FLUMES 

Freeboard,  depth,  and  area  for  different  conditions  of  flow,  and  multipliers 
for  other  values  of  n.     For  use  with  Fig.  29. 


FREEBOARD  AND  DEPTH  OF  FLOW  IN  FEET  AND 

AREA  IN  SQUARE  FEET 

I 

ade  Number 

Diameter 
of 
Flume 

|! 

IJK/8 

Flow  .437  D 
•  for  V  1.024 
•  for  Q  1.08J 

M 

Ml 

MULTIPLIERS 
FOR  OTHER 
VALUES 
OF  n 

jr  of  Flume  in  '. 

£ 

llii 

1111 

ill! 

iff! 

feQSS 

if 

I 

Free- 

Depth 

Free- 

Depth 

Free- 

Depth 

Free- 

Depth 

n 

n 

n 

board 

&Area 

board 

&  Area 

board 

&Area 

board 

&Area 

.013 

.014 

.015 

18 

1'-  0" 

0.083 

0.417 

0.062 

0.437 

0.050 

0.450 

0.042 

0.458 

.903 

.822 

.746 

1.000 

0.31 

0.33 

0.34 

0.35 

24 

1'-  Si" 

0.106 

0.530 

0.080 

0.556 

0.064 

0.572 

0.053 

0.582 

.905 

.826 

.750 

1.271 

0.50 

0.54 

0.55 

0.57 

36 

r-ii" 

0.160 

0.800 

0.120 

0.840 

0.096 

0.864 

0.080 

0.880 

.908 

.832 

.762 

1.920 

1.13 

1.21 

1.25 

1.28 

48 

2'-  6|" 

0.212 

1.06 

0.159 

1.11 

0.127 

1.14 

0.106 

1.17 

.910 

.836 

.768 

2.542 

2.01 

2.15 

2.22 

2.27 

60 

3'-  2J" 

0.265 

1.33 

0.199 

1.40 

0.159 

1.44 

0.132 

1.46 

.912 

.839 

.773 

3.190 

3.13 

3.35 

3.46 

3.54 

72 

3'-10" 

0.320 

1.60 

0.239 

1.68 

0.192 

1.72 

0.160 

1.76 

.913 

.842 

.777 

3.833 

4.52 

4.84 

5.00 

5.12 

84 

4'-  5J" 

0.371 

1.86 

0.278 

1.95 

0.223 

2.01 

0.186 

2.04 

.914 

.844 

.780 

4.458 

6.16 

6.60 

6.81 

6.97 

96 

5'-  1" 

0.423 

2.12 

0.317 

2.22 

0.254 

2.29 

0.212 

2.33 

.915 

.846 

.782 

5.083 

8.03 

8.60 

8.87 

9.10 

108 

5'-  8}" 

0.477 

2.39 

0.358 

2.51 

0.286 

2.58 

0.238 

2.63 

.916 

.847 

.784 

5.729 

10.17 

10.90 

11.2 

11.6 

120 

6  —  4j 

0.530 

2.66 

0.398 

2.79 

0.318 

2.87 

0.265 

2.92 

.917 

.848 

.786 

6.375 

12.53 

13.40 

13.8 

14.2 

132 

7'-  0" 

0.583 

2.92 

0.437 

3.06 

0.350 

3.15 

0.292 

3.21 

.918 

.849 

.788 

7.000 

15.18 

16.2 

16.8 

17.2 

144 

7'_  7j" 

0.637 

3.19 

0.478 

3.35 

0.382 

3.44 

0.318 

3.51 

.918 

.850 

.790 

7.646 

18.10 

19.4 

20.0 

20.5 

156 

8'-  4" 

0.695 

3.47 

0.520 

3.65 

0.417 

3.75 

0.348 

3.82 

.919 

.851 

.791 

8.333 

21.55 

23.1 

23.8 

24.4 

168 

8'-ll" 

0.743 

3.72 

0.557 

3.90 

0.445 

4.01 

0.372 

4.09 

.919 

.852 

.792 

8.920 

24.66 

26.4 

27.3 

27.9 

180 

9'-  6J" 

0.797 

3.98 

0.598 

4.19 

0.479 

4.30 

0.398 

4.38 

.919 

.853 

.793 

9.562 

28.36 

30.4 

31.3 

32.1 

192 

10'-  2" 

0.847 

4.24 

0.635 

4.45 

0.508 

4.58 

0.424 

4.66 

.920 

.853 

.793 

10.167 

32.10 

34.3 

35.5 

36.3 

204 

lO'-lO" 

0.903 

4.51 

0.677 

4.74 

0.542 

4.87 

0.452 

4.97 

.920 

.854 

.794 

10.833 

36.36 

38.9 

40.2 

41.2 

216 

11'-  5i" 

0.955 

4.77 

0.717 

5.01 

0.573 

5.16 

0.478 

5.25 

.920 

.855 

.795 

11.458 

40.80 

43.7 

45.1 

46.2 

228 

12'-  1" 

1.006 

5.03 

0.755 

5.29 

0.605 

5.44 

0.503 

5.54 

.921 

.855 

.796 

12.083 

45.40 

48.6 

50.2 

51.4 

240 

12'-  8f" 

1.060 

5.30 

0.796 

5.57 

0.636    5.73 

0.530 

5.84 

.921 

.856 

.797 

12.729 

50.35 

53.9 

55.7 

57.0 

NOTE. — In  the  columns  marked 
lower  figure  is  the  area. 


"  Depth  and  Area,"  the  upper  figure  is  the  depth  and  the 


HYDRAULIC   DIAGRAMS   AND   TABLES 


167 


Steel  Flumes 


?    Diameter  of  Flumes  v 


•01       1    1    1    I/I   1   1  '  [  1  1  !  I 

PJJMI  |i|[|||[n  ||  —  |\i   | 

y!  s 

II  III  ILIs^' 

.009      -~-j  — 
.008      --CX---        --I 

!:::!:!;::  pz  = 

S        t-  - 

:S^zi::jH: 

.007      -{-  *\  ?- 

--•L  :  jjj-  — 

--f^-- 

006      2            -     I  .  5  J  !  .  . 

IliN 

2     ss 

s 

'  „ 

\ 

ss              ^     ssx 

005                                1- 

^v                                            "S 

2 

V^       /                 ^ 

V_ 

^^ 

^v^ 

i^s 

.004      -  —  5  f-  

x        Z 

^s 

Z  Vy-<    > 

H'  Ttnil  —  —  n  — 

j  ^T--l^p 

"SSS^v,^SS       SS»^2"J 

;;^P^BI 

.0035    EEEl5*E  =  EJ 

.0025   =  =  |E:EE:I::3 

|||EEEEEEg 

S  E  i 

.002      -^  
.0015     s^-- 

M                          ^ 

^: 

--v,-  3  
.    ..      S2 

III* 

\ 

y        ^  " 

s       7 

.001                       -  -  -  s  -  -  - 

?i-3 

•  •  •  !|   L 

.0009    -                      J's- 
0008                                      S 

...TIi             £ 

i[i!l 

/    *%    / 

0007 

X                                              / 

/       ^  j 

L               I 

ft                   / 

cs 

::::::  | 

(IflOfi                                 / 

t 

1  L 

L          N^ 

1  ^ 

/            ^ 

•«s  f 

1  1      "s 

7 

7^         / 

1***  T 

Hl)iiii|ini 

j|!J!!!Jjrt" 

.0002  y-s^-- 

•-/-—    •—/- 

"  "  ?                 7 

|||  |e',/, 

.00015  -                   :.:i(. 

::::     ;  ;•     

t 

7          7'n" 

Svs 

/ 

~f 

i  £             X 

^               Z 

.0001        —L-      -L.. 

7 

^                 / 

T! 

1.5          2       2.5     3    3.5  4        5      6      7    8    9  10 
Discharge  (c.f.s.) 


13          20      25    30 


FIG.  29  (Part  1  of  2).  —  Discharge   of   Semicircular  Steel  Flumes. 
(Explanation  page  81.) 


168 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


TABLE  24 

SEMICIRCULAR  STEEL  FLUMES  FLOWING  PARTLY  FULL 

(KUTTER  FORMULA) 

Values  by  which  velocity  and  discharge  of  steel  flumes  given  by  Fig.  29 
should  be  multiplied  to  obtain  the  velocity  and  discharge  of  the  same 
flume  with  the  proportionate  depth  (ratio  of  depth  to  diameter)  given  in  the 
first  column. 


Propor- 
tionate 

D  = 

IFt. 

D  = 

2  Ft. 

D  = 

4  Ft. 

D  = 

6  Ft. 

D  = 

10  Ft. 

Depth 

Vel'ty 

Dis'ge 

V 

Q 

V 

Q 

V 

Q 

V 

Q 

.10 

.367 

.0485 

.384 

.0508 

.403 

.0533 

.412 

.0545 

.420 

.0555 

.11 

.395 

.0602 

.412 

.0628 

.431 

.0654 

.441 

.0666 

.449 

.0678 

.12 

.424 

.0730 

.441 

.0761 

.458 

.0790 

.468 

.0804 

.475 

.0818 

.13 

.451 

.0872 

.468 

.0908 

.486 

.0940 

.494 

.0953 

.499 

.0967 

.14 

.477 

.103 

.494 

.107 

.511 

.110 

.519 

.112 

.524 

.113 

.15 

.502 

.119 

.520 

.124 

.536 

.128 

.544 

.129 

.550 

.131 

.16 

.526 

.138 

.544 

.142 

.560 

.147 

.568 

.148 

.573 

.150 

.17 

.552 

.157 

.567 

.162 

.583 

.167 

.592 

.169 

.597 

.171 

.18 

.576 

.178 

.590 

.183 

.607 

.188 

.615 

.190 

.620 

.192 

.19 

.599 

.200 

.613 

.206 

.630 

.211 

.638 

.213 

.642 

.215 

.20 

.622 

.224 

.636 

.230 

.651 

.235 

.659 

.238 

.663 

.239 

.21 

.644 

.248 

.658 

.254 

.672 

.260 

.680 

.263 

.684 

.265 

.22 

.665 

.274 

.678 

.280 

.692 

.287 

.700 

.289 

.703 

.291 

.23 

.686 

.301 

.698 

.308 

.711 

.315 

.718 

.317 

.722 

.319 

.24 

.707 

.329 

.718 

.336 

.730 

.342 

.737 

.347 

.740 

.346 

.25 

.727 

.359 

.738 

.367 

.748 

.370 

.755 

.375 

.758 

.376 

.26 

.746 

.390 

.756 

.397 

.767 

.400 

.774 

.405 

.776 

.407 

.27 

.766 

.423 

.774 

.428 

.784 

.433 

.791 

.438 

.793 

.437 

.28 

.785 

.457 

.793 

.461 

.802 

.467 

.808 

.471 

.811 

.470 

.29 

.803 

.490 

.811 

.494 

.819 

.500 

.825 

.504 

.827 

.503 

.30 

.821 

.524 

.827 

.530 

.837 

.536 

.841 

.537 

.843 

.538 

.31 

.837 

.558 

.843 

.567 

.852 

.572 

.856 

.573 

.858 

.574 

.32 

.855 

.596 

.859 

.603 

.867 

.608 

.872 

.608 

.874 

.610 

.33 

.871 

.635 

.875 

.642 

.882 

.644 

.887 

.644 

.888 

.646 

.34 

.887 

.674 

.892 

.680 

.898 

.682 

.901 

.683 

.902 

.684 

.35 

.902 

.716 

.908 

.719 

.912 

.721 

.915 

.722 

.914 

.723 

.36 

.920 

.755 

.922 

.761 

.926 

.760 

.930 

.760 

.929 

.761 

.37 

.934 

.796 

.936 

.803 

.940 

.801 

.942 

.802 

.942 

.802 

.38 

.949 

.838 

.951 

.844 

.953 

.842 

.956 

.843 

.955 

.843 

.39 

.964 

.880 

.965 

.886 

.966 

.884 

.968 

.884 

.968 

.884 

.40 

.978 

.925 

.978 

.928 

.980 

.928 

.980 

.928 

.981 

.928 

.41 

.991 

.970 

.991 

.970 

.992 

.970 

.992 

.970 

.993 

.970 

.417 

.000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

.000 

.000 

.42 

.005 

1.014 

1.003 

1.013 

1.003 

1.013 

1.004 

1.013 

.004 

.013 

.43 

.017 

.058 

.016 

1.057 

1.015 

1.057 

1.016 

.057 

.014 

.057 

.44 

.030 

.105 

.028 

1.105 

1.026 

1.102 

1.027 

.102 

.023 

.102 

.45 

.044 

.153 

.040 

1.153 

1.038 

1.149 

1.038 

.145 

.034 

.145 

.46 

.057 

.200 

.051 

1.200 

1.049 

1.195 

1.048 

.192 

.045 

.192 

.47 

.068 

.248 

.062 

1.247 

1.060 

1.242 

1.058 

.240 

.055 

.239 

.48 

.079 

.295 

.073 

1.294 

1.070 

1.287 

1.068 

1.283 

.064 

1.282 

.49 

.090 

1.342 

.084 

1.341 

1.079 

1.335 

1.078 

1.330 

1.073 

1.327 

.50 

.101 

1.393 

.094 

1.389 

1.089 

1.380 

1.087 

1.377 

1.082 

1.373 

NOTE. — For  any  diameter  greater  than  10  feet  that  is  likely  to  be  used  in  practice,  the 
multipliers  are  practically  the  same  as  for  the  10  feet  diameter. 

There  is  a  slight  variation  with  the  slope  that  is  not  accounted  for  in  the  above  table.  For 
slopes  greater  than  .0005  the  error  is  usually  less  than  one  per  cent.  For  flatter  slopes  the  error 
is  somewhat  greater. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


169 


Diameter  of  Flumes 


Steel  Flumes 
^=.012 


.0001 


30         40      50    60    708090100  150       200     250300350400    5006007008001000 

Discharge  (c.f.s.) 

FIG.  29  (Part  2  of  2).— Discharge  of  Semicircular  Steel  Flumes. 


170 


WORKING   DATA  FOR  IRRIGATION   ENGINEERS 


Wood 
Pipe 


31 


oq  cj 


'2  O    O»    00     t-       «O         IS  -4*  CO  Cl  -I  — '  r-(    O  O     O       O 

8dJd  jo  tnSuexi  ^ooj  oooi  aod  ;aoj 


FIG.  30  (Part  1  of  2).— Flow  of  Water  in  Wood  Stave  Pipe. 
(See  pages  65  to  69.) 


HYDRAULIC   DIAGRAMS   AND   TABLES 


171 


O  OJ  00   f      «0      10 


„  3    «     3        -255 2 

QdJd  jo  "W  0001  -rod 


0  0 


FIG.  30  (Part  2  of  2).— Flow  of  Water  in  Wood  Stave  Pipe. 


172 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


Cast  Iron 
Pipe 


8di<i  jo  'M  000  [  J3d  1BQ£  ui  pt?8H  UOI^OTJ^ 

FIG.  31  (Part  1  of  2).— Flow  of  Water  in  New  Cast-Iron  and  Smooth 
Monolithic  Concrete  Pipe. 

(See  pages  65  to  69.) 


HYDRAULIC   DIAGRAMS   AND   TABLES 


173 


Cast  Iron 
Pipe 


FIG.  31  (Part  2  of  2).— Flow  of  Water  in  New  Cast-Iron  and  Smooth 
Monolithic  Concrete  Pipe. 


174 


WORKING  DATA   FOR   IRRIGATION   ENGINEERS 


s 
r 

to 
i] 

d 

>e 

J, 

:\l 

4-  ~- 

7 

^£ 

^s 

^•S-L1 

XL          ^ 

x 

[    V 

?  x~  ^ 

?- 

,7- 

00 

•' 

X 

s 

/    x^ 

0>  L^^ 

5 

/ 

-  T^s~  ~"1 

<? 

x  — 

2  Si 

N 

**•> 

^  / 

/^                 V 

x^ 

V 

Tyj;~ 

, 

5 

x 

to 

Z_  x 

/ 

^  V 

f 

x 

^  ^     r  '<?r- 

X 

*  *  " 

x 

^ 

7        x 

/ 

X  .,         / 

"X. 

0 

"xj^ 

'         X 

x 

/ 

jb 

XN^    7 

x> 

''*/\ 

! 

*S 

\ 

C^ 

y 

"   *» 

v 

/ 

X, 

J 

X 

^  / 

"•»  ^ 

1 

/ 

CO 

M  8 

-f 

:^:: 

/I 

5 

§ 

y    ^ 

x 

•x 

x 

v^ 

3| 
r?, 

^ 

j  j 

-^x- 

"*.2 
OJ.Q 

w 

9 

<  > 

1  [[It 

X 

. 

x 

if 

X^ 

~7 

^  N 

*x 

t    "  > 

x 

f 

or> 

^  ^ 

•  >i 

V. 

obo 

\^ 

/ 

s  s 

V 

x 

y 

o  g 

N^ 

/ 

s  ->J 

/ 

N 

^ 

^•o 

''  9^ 

^ 

^x 

/ 

°» 

^ 

X 

v^ 

/ 

x 

^ 

^" 

/ 

^ 

\ 

X 

I 

o 

/ 

CO 

o 

M 

0 
M 

.  _  t 

||!|! 

:::::::z 

..,,_. 

C^ 

3 

. 

^ 

rH 

<ff 

«5 

9  05    0 

« 

«      2 

03 

-H    0 

s  s 

i 

< 

1 

1- 

° 

FIG.  32  (Part  1  of  2).— Flow  of  Water  in  New  Asphalted  Riveted  Steel 
and  Jointed  Concrete  Pipe. 

(See  pages  65  to  69.) 


HYDRAULIC   DIAGRAMS   AND   TABLES 


175 


if    (O      to        •&  co      w        ci  ta  i-i  o»  oo    b-    <o      10       •*£ 

060660          6  6 

oditi  jo  '^j  OOOT  JQ^  ^^^il  UI  P^^H  noi^ou j[ 

FIG.  32  (Part  2  of  2).— Flow  of  Water  in  New  Asphalted  Riveted  Steel 
and  Jointed  Concrete  Pipe. 


176 


WORKING   DATA  FOR  IRRIGATION   ENGINEERS 


Different  Values  of  n 


•  010 


.015  .020  .025 

Values  of  Kutter's  "n" 


.035       .040 


FlG.  33.— Relative  Velocities  and  Slopes  for  Different  Values  of  "n. 
(Explanation  page  82.) 


HYDRAULIC   DIAGRAMS   AND   TABLES 


177 


H  =Head  in  Feet 
1          1.5      2    2.5   3  3.54     5    6    7  8  910          15      20    25  303540    50  60  7080  100 


0.9 

Q3  L^IXI  *  r\  r\  \A\m\jnx\jn\\w\\\\s\    i    i    i   ............  i  i  i  I  i  i  1  1  1  1  iiniiiiiii  ..........  I  .....  | 

.01        .015    .02.025.03     .04.05.06.07.08.1         .15      .2    .25.3.35.4    .5.6.7.8.91 
H  =Head  in  Feet 

FIG.  34.—  Theoretical  Velocity  Head  (Upper  line  of  each  group). 
This  diagram  also  gives  the  loss  of  head  through  orifices,  sluice-gates,  pipe 
intakes,  etc.,  for  a  given  coefficient  of  discharge:  Hf  =-j=r2  — 


of  Fig.  34 
Problem  : 

What  is  the  theoretical  velocity  generated  by  a  head  of 
.05  foot? 
Solution: 

At  the  intersection  of  the  upper  line  of  the  lower  group 


178  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

with  the  vertical  line  representing  H  =  .05  on  the  lower 
scale,  read  V  =  1.8  feet  per  second. 

Problem : 

What  is  the  theoretical  head  required  to  generate  a 
velocity  of  40  feet  per  second? 

Solution: 

At  the  intersection  of  the  upper  line  of  the  upper  group 
with  the  horizontal  line  representing  V  =  40,  read  on  the 
upper  scale  H  =  25  feet. 

Problem : 

What  total  head  is  required  to  force  water  through  an 
opening,  whose  coefficient  of  discharge  is  0.75,  with  a  velocity 
of  5  feet  per  second? 

Solution: 

At  the  intersection  of  the  horizontal  line  for  V  —  5  with 
the  inclined  line  marked  .75  (found  in  the  lower  group),  read 
on  the  lower  scale  H  =  0.7  foot. 

NOTE. — The  velocity  used  in  this  problem  is  that  obtained 
by  dividing  the  discharge  by  the  full  area  of  the  opening,  and  is 
not  the  actual  velocity  at  the  contracted  section,  which,  in  this  case, 
would  be  more  nearly  0.98  V20  x  0.7  =  6.7. 

Use  of  Fig.  35 
Problem : 

What  is  the  discharge  of  a  sluice  opening  4  feet  square 
having  contraction  suppressed  on  bottom  and  two  sides  when 
the  difference  in  elevation  of  water  surface  above  and  below 
the  opening  is  0.5  foot? 

Solution : 

The  area  of  this  opening  is  16  square  feet.  At  the  inter- 
section of  the  horizontal  line  for  H  =  0.5  with  the  imaginary 
line  for  area  =  16  we  read  on  the  lower  scale  Q  =  55  c.  f.  s. 
for  a  standard  sharp-edged  orifice;  multiplying  this  by  1.29 
we  get  71  c.  f.  s.  as  the  discharge  for  the  sluice  opening  in 
question. 


HYDRAULIC  DIAGRAMS   AND   TABLES 


179 


Submerged  Orifices 


i 


-b"- 


SOS 
0 


o  .g 


SSSfe  g  8J 

6  o*  d  o    o    d 


FIG.  35. — Discharge  of  Sharp-edged  Submerged  Orifices.    Q  =  0.61  A  \/2~gH 

Approximate  multipliers  of  discharge  for  Sluice  Gates: 

With  bottom  contraction   suppressed  =  1.07  (coeff.  of  discharge  =  0.65) 

With  bottom  and  one  side  suppressed  =  1.14  (coeff.  of  discharge  =  0.70) 

With  bottom  and  two  sides  suppressed  =  1.29  (coeff.  of  discharge  =  0.79) 

With  all  sides  suppressed  =  1.56  (coeff.  of  discharge  =  0.95) 


180 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


TABLE  25 

COEFFICIENTS  C'  TO  BE  APPLIED  TO  A  DISCHARGE  GIVEN  BY  FIGS.  36  AND 
37  FOR  A  HEAD  H  TO  GIVE  DISCHARGE  OF  SAME  WEIR  SUBMERGED, 

COMPUTED  FROM  THE  FORMULA  C'  =  -~|-  =      m  *  •    n  IS  HERSCHEL'S 
COEFFICIENT  FOR  SUBMERGED  WEIRS 


1 

d-f-H? 

0.00 

0.01 

0.02 

0.03 

0.04 

0.05 

0.06 

0.07 

0.08 

0.09 

1 

Tenths  S 

0.0 

1.000 

1.006 

1.009 

1.009 

1.011 

1.011 

1.011 

1.009 

1.009 

1.007 

.1 

1.007 

1.005 

1.003 

1.000 

.997 

.994 

.991 

.988 

.983   .981 

.2 

.978 

.973 

.970 

.966 

.963 

.958 

.955 

.951 

.946 

.942 

.3 

.939 

.935 

.931 

.926 

.921 

.917 

.913 

.909 

.903 

.900 

.4 

.895 

.891 

.885 

.881 

.875 

.871 

.865 

.859 

.854   .848 

.5 

.842 

,837 

.831 

.825 

.819 

.812 

.806 

.799 

.792   .785 

.6 

.778 

.771 

.764 

.756 

.748 

.740 

.733 

.724 

.715 

.707 

.7 

.698 

.689 

.680 

.670 

.660 

.649 

.639 

.626 

.615 

.603 

.8 

.589 

.576 

.562 

.547 

.531 

.517 

.501 

.486 

.469 

.453 

.9 

.435 

.416 

.396 

.375 

.351 

.323 

.293 

.255 

.209 

.144 

To  use  this  table,  read  the  discharge  from  Fig.  36  or  37  for 
free  fall  and  multiply  by  the  appropriate  coefficient  taken  from 
the  table  to  obtain  the  discharge  of  same  weir  with  crest  sub- 
merged to  a  depth  d,  below  downstream  water  surface. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


181 


&S 


\\ 


\\\ 


\\\ 


\\\ 


IS 


K 


Cippoletti  WeirS 


' 


3  I 


to      e^         M 


S 
FIG.  36.— Discharge  of  Standard  Cippoletti  Weirs.    £  =  3.37  L 


182 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


TABLE  26 

COEFFICIENTS  C  TO  BE  APPLIED  TO  A  DISCHARGE  TAKEN  FROM  FIGS.  36  AND 
37  FOR  A  HEAD  H,  TO  OBTAIN  THE  DISCHARGE  OF  THE  SAME  WEIR 
WHEN  A  VELOCITY  OF  APPROACH  v  EXISTS 

(h  =  velocity  of  head). 


V 

h 

hi 

H 

0.2 

0.4 

0.6 

0.8 

1.0 

1.5 

2.0 

2.5 

3.0 

3.5 

4.0 

5.0 

0.4  

0.0025 

0.0002 

1.014 

1.007 

1.004  1.004 

1.004 

1.002 

1.002 

1.002 

1.001 

1.001 

1.001 

1.001 

0.5  

.0039 

.0003 

1.02711.013  1.009:1.006 

1.006 

1.004  1.003 

1.002 

1.002 

1.002 

1.001 

1.001 

0.6  

.0056 

.0005 

1.037(1.019  1.013  1.009!l.008 

1.005 

1.004 

1.003 

1.003 

1.002 

1.002 

1.002 

0.7  

.0076 

.0007 

1.05011.026  1.017  1.013  1.011 

1.007 

1.006 

1.004 

1.004 

1.003 

1.003 

1.002 

0.8  

.0099 

.0010 

1.064J1.033  1.022;1.016  1.014 

1.009 

1.007 

1.006 

1.005 

1.004 

1.003 

1.003 

0.9  

.0126 

.0014 

1.082  1.042 

1.029  1.021 

1.018 

1.012 

1.009 

1.007 

1.006 

1.005 

1.005 

1.004 

1.0  

.0155 

.0019 

1.098 

1.051 

1.034 

1.027 

1.022 

1.015 

1.011 

1.009 

1.007 

1.006 

1.005 

1.005 

1.1  

.0188 

.0025 

1.122  1.062 

1.041 

1.031 

1.Q26 

1.017 

1.013 

1.011 

1.009 

1.008 

1.007 

1.006 

1.2  

.0224 

.0033 

1.141  1.072 

1.049 

1.037 

1.031 

1.021 

1.016 

1.013 

1.011 

1.009 

1.008 

1.007 

1.3  

.0263 

.0041 

1.163 

1.084 

1.057 

1.043 

1.036 

1.024 

1.018 

1.015 

1.012 

1.011 

1.009 

1.008 

1.4  

.0305 

.0051 

1.186 

1.096 

1.066 

1.050 

1.041 

1.028 

1.021 

1.017 

1.014 

1.012 

1.011 

1.010 

1.5  

.0350 

.0064 

1.208 

1.109 

1.075 

1.057 

1.047 

1.032 

1.024 

1.019 

1.016 

1.014 

1.012 

1.011 

1.6  

.0398 

.0079 

1.225 

1.122 

1.084 

1.065 

1.052 

1.035 

1.027 

1.022 

1.018 

1.016 

1.014 

1.012 

1.7  

.0449 

.0095 

1.254 

1.135 

1.093 

1.071 

1.059 

1.040 

1.031 

1.025 

1.021 

1.018 

1.016 

1.014 

1.8  

.0504 

.0111 

1.277 

1.149 

1.104 

1.080 

1.065 

1.045 

1.034 

1.027 

1.023 

1.020 

1.017 

1.016 

1.9  

.0561 

.0132 

1.308 

1.165 

1.115 

1.089 

1.072 

1.049 

1.038 

1.030 

1.026 

1.022 

1.019 

1.017 

2.0  

.0622 

.0154 

1.335 

1.181 

1.126 

1.097 

1.079 

1.055 

1.042 

1.034 

1.028 

1.025 

1.021 

1.019 

2.1  

.0686 

.0179 

1.363 

1.197 

1.137 

1.106 

1.087 

1.060 

1.046 

1.037 

1.031 

1.027 

1.024 

1.021 

2.2  

.0752 

.0206 

1.391 

1.213 

1.149 

1.118 

1.094 

1.065 

1.050 

1.039 

1.034 

1.029 

1.026 

1.023 

2.3  

.0822 

.0235 

.420 

1.231 

1.161 

1.124 

1.102 

1.071 

1.054 

1.044 

1.037 

1.032 

1.028 

1.025 

2.4  

.0895 

.0268 

.449 

1.248 

1.176 

1.134 

1.110 

1.077 

1.059 

1.047 

1.040 

1.034 

1.030  1.027 

2.5  

.0972 

.0303 

.480 

1.266 

1.187 

1.145  1.119 

1.083 

1.063 

1.051 

1.043 

1.037 

1.033  1.029 

2.6  

.1051 

.0340 

.511 

1.285 

1.200 

1.1551.128 

1.088  1.068 

1.055 

1.046 

1.040 

1.035  1.032 

2.7  

.1133 

.0381 

.542  1.303  1.213  1.166  1.137  1.095 

1.073 

1.059 

1.050 

1.043 

1.038 

1.034 

2.8  

.1219 

.0426 

1.573  1.322  1.228  1.178  1.146  1.100  1.078 

1.063 

1.053 

1.046 

1.041 

1.036 

2.9  

.1307 

.0472 

1.606  1.341 

1.242  1.189  1.155  1.108  1.083 

1.067 

1.057 

1.049 

1.043 

1.039 

3.0  

0.1399 

0.0524 

1.63711.361 

1.256  1.199  1.165 

1.115 

1.088 

1.072 

1.061 

1.053 

1.046 

1.041 

| 

To  use  this  table,  read  the  discharge  from  Figs.  36  or  37  for  the  measured 
head  and  multiply  by  the  appropriate  coefficient  taken  from  the  above  table 
to  obtain  the  discharge  when  a  velocity  of  approach  v  exists. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


183 


Rectangular  Weirs 


FIG.  37. — Discharge  of  Standard  Suppressed  Rectangular  Weirs  —  Q  =  3.33LH% 

and 

Discharge  of  Standard  Contracted  Rectangular  Weirs  —  Q  =  3.33  Llf/>2 

-    .666  H% 

NOTE. — For  Contracted  Weirs  this  diagram  is  not  accurate  for  heads  greater 
than  one-third  the  crest-length. 


184  WORKING  DATA  FOR   IRRIGATION   ENGINEERS 

TABLE  27 

DISCHARGE  OVER  SHARP-CRESTED  VERTICAL  WEIRS  WITHOUT  END  CON- 
TRACTIONS, IN  CUBIC  FEET  PER  SECOND  PER  FOOT  OF  LENGTH  OF  WEIR 
FOR  SMALL  HEADS 


Head, 
in 
Feet 

Weir 
0.5  Ft. 
High 

Weir 
0.75  Ft. 
High 

Weir 
1.00  Ft. 
High 

Weir 
1  .  50  Ft. 
High 

Weir 
2.00  Ft. 
High 

Weir 
3.00  Ft. 
High 

Weir 
4.00  Ft. 
High 

Weir  • 
6.00  Ft. 
High 

0  200 

0  315 

0  314 

0  313 

0  312 

0  311 

0.310 

0.309 

0  205 

0  327 

0  326 

0  325 

0.324 

0.323 

0.322 

0.321 

0.210 
0  215 

0.340 
0  352 

0.337 
0  351 

0.336 
0  350 

0.335 
0  348 

0.334 
0  347 

0.333 
0  346 

0.332 
0  346 



0.220 
0  225 

0.365 
0  377 

0.363 
0  375 

0.360 
0  372 

0.359 
0  370 

0.357 
0  369 

0.356 
0  368 

0.355 
0  367 

0  230 

0  392 

0  388 

0  385 

0  383 

0  382 

0  381 

0  380 

0.235 
0  240 

0.404 
0  420 

0.400 
0  415 

0.398 
0  412 

0.396 
0  408 

0.394 
0  406 

0.393 
0  405 

0.392 
0  404 



0  245 

0  433 

0  427 

0  425 

0  422 

0  420 

0  417 

0  416 

0  250 

0  446 

0  442 

0  438 

0  435 

0  434 

0  432 

0  430 

0  955 

0  460 

0  453 

0  450 

0  447 

0  445 

0  443 

0  442 

0.260 
0.265 
0  270 

0.475 
0.490 
0  503 

0.468 
0.483 
0  497 

0.465 
0.478 
0  493 

0.460 
0.475 
0  488 

0.458 
0.473 
0  486 

0.456 
0.470 
0  484 

0.455 
0.468 
0  483 



0.275 
0.280 
0.285 
0.290 
0  295 

0.515 
0.530 
0.546 
0.560 
0  576 

0.508 
0.524 
0.537 
0.552 
0  566 

0.505 
0.518 
0.532 
0.547 
0  560 

0.501 
0.514 
0.526 
0.544 
0  555 

0.498 
0.510 
0.523 
0.540 
0  552 

0.496 
0.507 
0.520 
0.535 
0  548 

0.495 
0.506 
0.517 
0.533 
0  546 



0.300 
0.305 
0  310 

0.595 
0.610 
0  625 

0.584 
0.595 
0  612 

0.576 
0.588 
0  605 

0.570 
0.582 
0  598 

0.566 
0.577 
0  595 

0.563 
0.575 
0  590 

0.560 
0.572 
0  586 

0.315 
0  320 

0.640 
0  655 

0.627 
0  645 

0.620 
0  636 

0.613 
0  630 

0.608 
0  625 

0.605 
0  620 

0.602 
0  617 



0  325 

0  670 

0  655 

0  650 

0  641 

0  636 

0  632 

0  630 

0'.330 
0.335 
0  340 

0.690 
0.705 
0  720 

0.672 
0.690 
0  705 

0.665 
0.680 
0  697 

0.656 
0.670 
0  688 

0.652 
0.665 
0  683 

0.647 
0.660 
0  675 

0.645 
0.657 
0  673 

0.345 
0  350 

0.738 
0  755 

0.720 
0  735 

0.710 
0  726 

0.703 
0  717 

0.696 
0  712 

0.692 
0  705 

0.687 
0  702 



0.355 
0.360 
0.365 
0.370 
0  375 

0.770 
0.790 
0.805 
0.824 
0  840 

0.752 
0.772 
0.786 
0.802 
0  817 

0.743 
0.760 
0.775 
0.792 
0  805 

0.732 
0.750 
0.764 
0.780 
0  795 

0.725 
0.745 
0.757 
0.775 
0  790 

0.720 
0.737 
0.750 
0.766 
0  782 

0.717 
0.733 
0.746 
0.762 

0  777 



0  380 

0  860 

0  836 

0  825 

0  813 

0  805 

0  798 

0  795 

0.385 
0.390 
0  395 

0.875 
0.896 
0  910 

0.853 
0.870 
0  885 

0.840 
0.857 
0  870 

0.826 
0.845 
0  860 

0.820 
0.837 
0  852 

0.810 
0.830 
0  845 

0.806 
0.825 
0  838 

0.400 
0.405 
0.410 
0.415 
0.420 

0.930 
0.950 
0.970 
0.990 
1.005 

0.905 
0.922 
0.940 
0.956 
0.975 

0.893 
0.910 
0.925 
0.943 
0.958 

0.875 
0.895 
0.910 
0.925 
0.943 

0.870 
0.885 
0.903 
0.917 
0.935 

0.860 
0.875 
0.895 
0.908 
0.924 

0.855 
0.870 
0.885 
0.903 
0.917 

0.850 
0.860 
0.876 
0.895 
0.910 

NOTE. — This  table  covers  the  same  ground  as  the  first  fifteen  lines  of  Table  28  but  in 
greater  detail.  This  table  should  not  be  used  where  the  weir  is  submerged,  nor  unless  the 
overfalling  sheet  is  aerated  on  the  downstream  face  of  the  weir.  This  table  is  reproduced 
by  permission  of  the  author,  Prof.  R.  R.  Lyman  of  the  University  of  Utah.  It  was  originally 
published  in  Trans.  Am.  Soc.  C.  E.,  1914,  and  in  a  Bulletin  of  the  U.  of  U. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


185 


TABLE  27  (Continued) 
DISCHARGE  IN  CUBIC  FEET  PER  SECOND  PER  FOOT  OF  LENGTH  OF  WEIR 


Head, 
in 
Feet 

Weir 
0.5  Ft. 
High 

Weir 
0.75  Ft. 
High 

Weir 
1.00  Ft. 
High 

Weir 
1  .  50  Ft. 
High 

Weir 
2.00  Ft. 
High 

Weir 
3.00  Ft. 
High 

Weir 
4.00  Ft. 
High 

Weir 
6.00  Ft. 
High 

0.425 

,020 

0.995 

0.977 

0.963 

0.952 

0.942 

0.935 

0.926 

0.430 

.045 

1.010 

0.996 

0.980 

0.970 

0.957 

0.952 

0.945 

0.435 

.065 

1.030 

1.010 

0.996 

0.986 

0.975 

0.970 

0.960 

0.440 

.083 

1.045 

1.026 

.010 

1.000 

0.992 

0.985 

0.976 

0.445 

.100 

1.063 

1.045 

.026 

1.015 

1.005 

1.000 

0.994 

0.450 

.120 

1.080 

1.060 

.040 

1.030 

1.015 

1.010 

.030 

0.455 

1.140 

1.100 

1.080 

.057 

1.047 

1.035 

1.023 

.016 

0.460 

1.164 

1.125 

1.105 

.085 

1.074 

1.056 

1.050 

.043 

0.465 

1.185 

1.140 

.120 

.100 

.090 

.075 

1.067 

.057 

0.470 

.205 

1.163 

.143 

.120 

.106 

.095 

1.085 

.077 

0.475 

.230 

1.185 

.162 

.140 

.125 

.110 

1.105 

.096 

0.480 

.250 

1.205 

.185 

.160 

.150 

.133 

1.125 

.115 

0.485 

.270 

1.223 

.200 

.175 

.163 

.150 

.140 

.130 

0.490 

.290 

1.245 

.220 

.200 

.183 

1.166 

.160 

.150 

0.495 

.310 

1.265 

.233 

.215 

.200 

1.186 

.176 

1.166 

0.500 

.335 

1.285 

.263 

.235 

1.220 

1.203 

.195 

1.185 

0.505 

.355 

1.300 

.280 

1.250 

1.236 

1.220 

.210 

1.202 

0.510 

.370 

1.320 

.296 

1.270 

1.257 

1.237 

.225 

1.220 

0.515 

.390 

1.340 

.317 

1.287 

1.274 

1.255 

.244 

1.235 

0.520 

.415 

1.360 

1.335 

1.305 

1.290 

1.273 

1.260 

.252 

0.525 

.440 

1.380 

1.355 

1.325 

1.310 

1.290 

1.280 

.274 

0.530 

.465 

1.405 

1.375 

1.346 

1.330 

1.310 

1.300 

.293 

0.535 

.490 

1.425 

1.400 

1.365 

1.353 

1.335 

1.320 

.310 

0.540 

.510 

1.440 

1.415 

1.385 

1.365 

.350 

1.336 

.327 

0.545 

.530 

1.465 

1.435 

1.403 

1.385 

.365 

1.355 

.345 

0.550 

.555 

1.490 

1.460 

1.425 

1.405 

.385 

.370 

.365 

0.555 

.575 

1.505 

1.475 

1.440 

.420 

.400 

.390 

1.380 

0.560 

.595 

1.525 

1.495 

1.460 

.435 

.415 

.405 

1.395 

0.565 

.616 

1.545 

1.515 

1.475 

.455 

.435 

.420 

1.410 

0.570 

.640 

1.570 

1.535 

1.500 

.475 

.455 

.440 

1.430 

0.575 

.665 

1.590 

1.555 

1.517 

.500 

.475 

.460 

1.450 

0.580 

.686 

1.610 

1.576 

1.537 

.517 

.495 

.480 

1.470 

0.585 

.713 

1.635 

1.605 

1.565 

.540 

.520 

.505 

1.495 

0.590 

.740 

1.670 

1.630 

1.590 

.570 

.545 

.530 

.523 

0.595 

.760 

1.685 

1.650 

1.605 

.585 

.560 

.543 

.535 

0.600 

.790 

1.700 

1.675 

1.625 

.605 

.580 

.565 

.555 

0.605 

.805 

1.730 

1.695 

1.655 

.627 

.605 

1.590 

.580 

0.610 

.830 

1.750 

1.715 

1.675 

.650 

.625 

1.610 

.600 

0.615 

.855 

.775 

1.735 

1.695 

.675 

.650 

1.630 

.620 

0.620 

.880 

.795 

1.760 

1.710 

.690 

.670 

1.650 

1.640 

0.625 

.905 

.815 

1.780 

.730 

.705 

.685 

1.670 

1.665 

0.630 

.930 

.845 

1.805 

.760 

.730 

.705 

1.694 

1.687 

0.635 

.955 

.875 

1.835 

.785 

.760 

.725 

1.710 

1.700 

0.640 

.980 

.900 

1.860 

.815 

.790 

.760 

.740 

1.730 

0.645 

2.010 

.915 

1.870 

.820 

.800 

.770 

.750 

.740 

0.650 

2.035 

.930 

1.890 

.840 

.810 

.780 

.760 

.750 

0.655 

2.060 

.960 

1.915 

.860 

.830 

.805 

.785 

.775 

0.660 

2.085 

.985 

1.945 

.890 

.865 

1.830 

.815 

.805 

0.665 

2.110 

2.005 

1.965 

.910 

.880 

1.850 

.830 

.820 

0.670 

2.135 

2.025 

1.980 

.930 

.900 

1.870 

.850 

.840 

186 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


TABLE  27  (Continued] 
DISCHARGE  IN  CUBIC  FEET  PER  SECOND  PER  FOOT  OF  LENGTH  OF  WEIR 


Head, 
in 
Feet 

Weir 
0  .  5  Ft. 
High 

Weir 
0.75  Ft. 
High 

Weir 
1.00  Ft. 
High 

Weir 
1.50  Ft. 
High 

Weir 
2.00  Ft. 
High 

Weir 
3.00  Ft. 
High 

Weir 
4.00  Ft. 
High 

Weir 
6.00  Ft. 
High 

0.675 

2.160 

2.055 

2.000 

1.945 

1.910 

1.880 

1.860 

1.850 

0.680 

2.185 

2.075 

2.030 

1.980 

1.945 

1.910 

1.895 

.885 

0.685 

2.210 

2.095 

2.050 

1.990 

1.960 

1.925 

1.905 

.895 

0.690 

2.240 

2.125 

2.075 

2.025 

1.990 

1.960 

1.935 

.925 

0.695 

2.260 

2.150 

2.095 

2.040 

2.005 

1.970 

1.945 

.930 

0.700 

2.295 

2.180 

2.130 

2.070 

2.030 

1.995 

1.975 

.965 

0.705 

2.325 

2.200 

2.155 

2.100 

2.065 

2.025 

2.000 

.985 

0.710 

2.350 

2.220 

2.170 

2.115 

2.085 

2.040 

2.020 

2.005 

0.715 

2.380 

2.250 

2.195 

2.140 

2.105 

2.060 

2.035 

2.025 

0.720 

2.410 

2.275 

2.220 

2.160 

2.125 

2.085 

2.060 

2.045 

0.725 

2.435 

2.300 

2.245 

2.180 

2.155 

2.115 

2.090 

2.080 

0.730 

2.465 

2.325 

2.270 

2.200 

2.175 

2.135 

2.110 

2.095 

0.735 

2.490 

2.350 

2.295 

2.230 

2.190 

2.150 

2.130 

2.120 

0.740 

2.520 

2.375 

2.320 

2.250 

2.210 

2.170 

2.140 

2.130 

0.745 

2.550 

2.405 

2.340 

2.275 

2.235 

2.200 

2.170 

2.160 

0.750 

2.585 

2.430 

2.375 

2.300 

2.260 

2.225 

2.190 

2.180 

0.755 

2.605 

2.455 

2.400 

2.325 

2.285 

2.245 

2.220 

2.200 

0.760 

2.640 

2.480 

2.415 

2.340 

2.300 

2.270 

2.240 

2.230 

0.765 

2.670 

2.510 

2.440 

2.370 

2.330 

2.290 

2.265 

2.255 

0.770 

2.700 

2.540 

2.470 

2.400 

2.350 

2.300 

2.285 

2.275 

0.775 

2.730 

2.560 

2.500 

2.420 

2.375 

2.330 

2.310 

2.300 

0.780 

2.760 

2.590 

2.515 

2.440 

2.400 

2.345 

2.330 

2.325 

0.785 

2.790 

2.610 

2.550 

2.460 

2.415 

2.365 

2.345 

2.335 

0.790 

2.820 

2.630 

2.570 

2.480 

2.430 

2.380 

2.360 

2.350 

0.795 

2.850 

2.660 

2.595 

2.510 

2.460 

2.410 

2.380 

2.365 

0.800 

2.890 

2.700 

2.625 

2.550 

2.500 

2.440 

2.410 

2.400 

0.805 

2.910 

2.730 

2.660 

2.575 

2.520 

2.465 

2.425 

2.410 

0.810 

2.940 

2.755 

2.680 

2.595 

2.545 

2.485 

2.445 

2.425 

0.815 

2.975 

2.780 

2.700 

2.610 

2.565 

2.505 

2.460 

2.440 

0.820 

3.010 

2.810 

2.735 

2.640 

2.590 

2.530 

2.500 

2.480 

0.825 

3.045 

2.840 

2.770 

2.670 

2.610 

2.560 

2.530 

2.510 

0.830 

3.070 

2.870 

2.790 

2.700 

2.640 

2,580 

2.550 

2.535 

0.835 

3.100 

2.905 

2.830 

2.730 

2.675 

2.610 

2.580 

2.565 

0.840 

3.130 

2.930 

2.840 

2.760 

2.695 

2.630 

2.600 

2.590 

0.845 

3.160 

2  .  950 

2.880 

2.785 

2.730 

2.650 

2.615 

2.605 

0.850 

3.190 

2.990 

2.910 

2.800 

2.750 

2.680 

2.650 

2.630 

0.855 

3.230 

3.015 

2.930 

2.840 

2.780 

2.710 

2.670 

2.650 

0.860 

3.260 

3.040 

2.960 

2.860 

2.800 

2.735 

2.700 

2.680 

0.865 

3.290 

3.070 

2.980 

2.880 

2.815 

2.750 

2.715 

2.695 

0.870 

3.320 

3.100 

3.010 

2.910 

2.840 

2.780 

2.740 

2.720 

0.875 

3.350 

3.120 

3.035 

2.930 

2.870 

2.795 

2.765 

2.750 

0.880 

3.395 

3.160 

3.070 

2.965 

2.900 

2.820 

2.790 

2.780 

0.885 

3.415 

3.180 

3.090 

2.980 

2.920 

2.840 

2.810 

2.790 

0.890 

3.445 

3.200 

3.120 

3.010 

2.940 

2.860 

2.825 

2.820 

0.895 

3.480 

3.235 

3.150 

3.040 

2.970 

2.895 

2.860 

2.845 

0.900 

3.520 

3.270 

3.180 

3.070 

3.000 

2.920 

2.890 

2.870 

0.905 

3.550 

3.300 

3.210 

3.100 

3.035 

2.940 

2.910 

2.890 

0.910 

3.580 

3.330 

3.235 

3.120 

3.055 

2.970 

2.930 

2.910 

0.915 

3.620 

3.360 

3.260 

3.155 

3.085 

3.000 

2.955 

2.935 

HYDRAULIC   DIAGRAMS   AND   TABLES 


187 


TABLE  27  (Continued) 
DISCHARGE  IN  CUBIC  FEET  PER  SECOND  PER  FOOT  OF  LENGTH  OF  WEIR 


Head, 
in 
Feet 

Weir 
0.5  Ft. 
High 

Weir 
0.75  Ft. 
High 

Weir 
1.00  Ft. 
High 

Weir 
1  .  50  Ft. 
High 

Weir 
2.00  Ft. 
High 

Weir 
3.00  Ft. 
High 

Weir 
4.00  Ft. 
High 

Weir 
6.00  Ft. 
High 

0.920 

3.655 

3.390 

3.290 

3.180 

3.110 

3.030 

2.980 

2.960 

0.925 

3.690 

3.420 

3.325 

3.210 

3.140 

3.055 

3.010 

2.990 

0.930 

3.720 

3.445 

3.350 

3.230 

3.160 

3.075 

3.030 

3.010 

0.935 

3.760 

3.480 

3.380 

3.250 

3.180 

3.100 

3.060 

3.040 

0.940 

3.800 

3.510 

3.405 

3.290 

3.210 

3.130 

3.080 

3.060 

0.945 

3.830 

3.540 

3.430 

3.315 

3.240 

3.150 

3.110 

3.090 

0.950 

3.870 

3.580 

3.470 

3.350 

3.260 

3.180 

3.140 

3.120 

0.955 

3.900 

3.610 

3.500 

3.380 

3.295 

3.200 

3.165 

3.140 

0.960 

3.940 

3.640 

3.540 

3.400 

3.325 

3.235 

3.190 

3.170 

0.965 

3.980 

3.680 

3.570 

3.430 

3.355 

3.260 

3.210 

3.190 

0.970 

4.010 

3.700 

3.590 

3.450 

3.370 

3.275 

3.235 

3.200 

0.975 

4.040 

3.740 

3.625 

3.490 

3.405 

3.310 

3.270 

3.250 

0.980 

4.080 

3.770 

3.650 

3.520 

3.430 

3.330 

3.290 

3.270 

0.985 

4.120 

3.800 

3.690 

3.555 

3.460 

3.365 

3.320 

3.300 

0.990 

4.150 

3.830 

3.710 

3.580 

3.480 

3.380 

3.340 

3.320 

0.995 

4.180 

3.850 

3.730 

3.590 

3.510 

3.400 

3.360 

3.330 

1.000 

4.230 

3.900 

3.780 

3.640 

3.555 

3.440 

3.400 

3.375 

1.010 

4.300 

3.970 

3.840 

3.710 

3.600 

3.500 

3.450 

3.420 

1.020 

4.380 

4.030 

3.900 

3.760 

3.670 

3.560 

3.500 

3.480 

1.030 

4.450 

4.100 

3.970 

3.820 

3.720 

3.600 

3.560 

3.540 

1.040 

4.520 

4.170 

4.040 

3.880 

3.780 

3.670 

3.620 

3.590 

1.050 

4.610 

4.240 

4.120 

3.950 

3.850 

3.730 

3.670 

3.650 

1.060 

4.800 

4.320 

4.180 

4.020 

3.910 

3.790 

3.740 

3.710 

1.070 

4.760 

4.370 

4.220 

4.070 

3.960 

3.830 

3.770 

3.750 

1.080 

4.820 

4.430 

4.280 

4.130 

4.010 

3.890 

3.820 

3.800 

.090 

4.900 

4.480 

4.340 

4.180 

4.060 

3.930 

3.870 

3.840 

.100 

4.980 

4.570 

4.420 

4.240 

4.140 

3.990 

3.940 

3.910 

.110 

5.060 

4.640 

4.480 

4.320 

4.190 

4.060 

4.000 

3.960 

.120 

5.150 

4.710 

4.560 

4.370 

4.240 

4.120 

4.050 

4.010 

.130 

5.220 

4.780 

4.610 

4.420 

4.300 

4.170 

4.100 

4.070 

.140 

5.300 

4.840 

4.670 

4.480 

4.360 

4.210 

4.160 

4.130 

1.150 

5.380 

4.910 

4.740 

4.560 

4.420 

4.270 

4.210 

4.180 

1.160 

5.450 

4.980 

4..  800 

4.610 

4.480 

4.330 

4.260 

4.220 

1.170 

5.510 

5.050 

4.870 

4.670 

4.540 

4.380 

4.320 

4.280 

1.180 

5.600 

5.130 

4.950 

4.740 

4.610 

4.440 

4.380 

4.340 

1.190 

5.680 

5.200 

5.000 

4.800 

4.660 

4.500 

4.420 

4.400 

.200 

5.780 

5.250 

5.075 

4.870 

4.720 

4.560 

4.480 

4.440 

.210 

5.860 

5.340 

4.150 

4.940 

4.780 

4.610 

4.540 

4.500 

.220 

5.940 

5.420 

5.250 

5.000 

4.860 

4.680 

4.610 

4.590 

.230 

6.000 

5.460 

5.270 

5.050 

4.910 

4.720 

4.640 

4.610 

.240 

6.100 

5.550 

5.360 

5.150 

4.980 

4.800 

4.720 

4.680 

.250 

6.200 

5.620 

5.430 

5.220 

5.050 

4.860 

4.780 

4.740 

.260 

6.275 

5.675 

5.500 

5.275 

5.100 

4.910 

4.830 

4.800 

.270 

5.750 

5.560 

5.325 

5.180 

4.970 

4.890 

4.850 

.280 



5.820 

5.620 

5.380 

5.225 

5.000 

4.940 

4.900 

.290 

5.900 

5  680 

5  450 

5  275 

5  075 

5.000 

4.960 

.300 

5.975 

5.775 

5.525 

5.350 

5.150 

5.050 

5.020 

.310 

6.060 

5.850 

5.600 

5.425 

5.225 

5.130 

5.080 

.320 

6.150 

5.920 

5.675 

5.500 

5.275 

5.200 

5.150 

1.330 



6.200 

6.000 

5.730 

5.550 

5.350 

5.250 

5.220 

188 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


TABLE  27  (Concluded) 
DISCHARGE  IN  CUBIC  FEET  PER  SECOND  PER  FOOT  OF  LENGTH  OF  WEIR 


Head, 
in 
Feet 

Weir 
0.5  Ft. 
High 

Weir 
0.75  Ft. 
High 

Weir 
1.00  Ft. 
High 

Weir 
1.50  Ft. 
High 

Weir 
2.00  Ft. 
High 

Weir 
3.00  Ft. 
High 

Weir 
4.00  Ft. 
High 

Weir 
6.00  Ft. 
High 

.340 

6.300 

6.050 

5.800 

5.620 

5.400 

5.320 

5.260 

.350 
.360 
.370 
.380 
.390 
.400 

6.375 
6.450 
6.505 
6.625 
6.700 
6.780 

6.130 
6.200 
6.300 
6.375 
6.450 
6.530 

5.875 
5.940 
6.000 
6.080 
6.150 
6.230 

5.675 
5.750 
5.820 
5.900 
5.960 
6.040 

5.460 
5.520 
5.580 
5.650 
5.725 
5.770 

5.370 
5.430 
5.500 
5.560 
5.625 
5.675 

5.320 
5.380 
5.450 
5.525 
5.575 
5.640 

.410 
.420 
.430 
.440 
.450 
.460 
470 

6.860 
6.950 
7.000 
7.075 
7.150 
7.250 
7  330 

6.620 
6.675 
6.750 
6.820 
6.900 
6.975 
7  050 

6.320 
6.375 
6.450 
6.520 
6.600 
6.660 
6  740 

6.100 
6.150 
6.220 
6.300 
6.360 
6.430 
6  500 

5.850 
5.920 
5.975 
6.030 
6.100 
6.150 
6  220 

5.760 
5.820 
5.875 
5.930 
6.000 
6.050 
6  120 

5.700 
5.760 
5.825 
5.880 
5.950 
6.000 
6  060 

480 

7  400 

7  130 

6  800 

6  508 

6  300 

6  175 

6  125 

.490 
.500 
.510 
.520 
.530 

7.480 
7.600 
7.660 
7.750 

7.825 

7.200 
7.300 
7.360 
7.450 
7.520 

6.850 
6.950 
7.020 
7.100 
7.160 

6.640 
6.720 
6.775 
6.850 
6.930 

6.330 
6.420 
6.500 
6.550 
6.640 

6.230 
6.300 
6.360 
6.450 
6.520 

6.160 
6.250 
6.300 
6.360 
6.460 

.540 
.550 
.560 
.570 
.580 
.590 

7.900 
7.980 
8.075 
8.150 
8.250 
8.300 

7.600 
7.660 
7.730 
7.820 
7.900 
7.960 

7.230 
7.300 
7.400 
7.450 
7.525 
7.560 

7.000 
7.040 
7.120 
7.180 
7.250 
7.300 

6.680 
6.740 
6.800 
6.860 
6.940 
6.975 

6.575 
6.625 
6.700 
6.740 
6.800 
6.850 

6.500 
6.560 
6.630 
6.680 
6.750 
6.780 

Table  28  gives  the  discharge  per  foot  of  length  over 
sharp-crested  vertical  weirs,  without  end  contractions,  of  heights 
2,  4,  6,  8, 10,  20,  and  30  feet,  computed  from  Bazin's  formula.  Al- 
though this  formula  is  based  on  data  obtained  from  experiments 
with  heads  not  greater  than  1.64  feet,  discharges  for  heads  of  4 
feet  and  less  computed  thereby  agree  within  2  per  cent  with 
those  obtained  by  use  of  the  Fteley  and  Stearns  formula.  The 
discharge  given  by  this  table  is  corrected  for  velocity  of  approach, 
and  the  head  to  be  used  is  that  observed  16  feet  or  more  upstream 
from  the  crest  of  the  weir. 


HYDRAULIC   DIAGRAMS   AND   TABLES 
TABLE  28 


189 


DISCHARGE  PER  FOOT  OF  LENGTH  OVER  SHARP-CRESTED  VERTICAL  WEIRS 
WITHOUT  END  CONTRACTIONS  * 


[Computed  from  the  formula  Q  =  (o.405  +  ^^)  (l  +  0.55 

Lh  \/2gh  (h  =  observed  head,  in  feet;  p  =  height  of  weir,  in  feet;  L  =  length 
of  crest,  in  feet;  Q  =  discharge,  in  second-feet.)] 


\p 
*\ 

2 

4 

6 

8 

10 

20 

30 

0.1 

0.13 

0.13 

0.13 

0.13 

0.13 

0.13 

0.13 

0.2 

.33 

.33 

.33 

.33 

.33 

.33 

.33 

0.3 

.58 

.58 

.58 

.58 

.58 

.58 

.58 

0.4 

.88 

.88 

.87 

.87 

.87 

.87 

.87 

0.5 

1.23 

1.21 

1.21 

1.21 

1.21 

1.20 

1.20 

0.6 

1.62 

1.59 

1.58 

1.58 

1.57 

1.57 

1.57 

0.7 

2.04 

1.99 

1.98 

1.98 

1.97 

1.97 

1.97 

0.8 

2.50 

2.43 

2.41 

2.41 

2.40 

2.40 

2.40 

0.9 

3.00 

2.90 

2.88 

2.86 

2.86 

2.85 

2.85 

1.0 

3.53 

3.40 

3.36 

3.35 

3.34 

3.33 

3.33 

1.1 

4.10 

3.93 

3.88 

3.86 

3.85 

3.84 

3.83 

1.2 

4.69 

4.48 

4.42 

4.40 

4.38 

4.36 

4.36 

1.3 

5.32 

5.07 

4.99 

4.96 

4.94 

4.92 

4.91 

1.4 

5.99 

5.68 

5.58 

5.55 

5.52 

5.49 

5.48 

1.5 

6.69 

6.30 

6.20 

6.16 

6.13 

6.08 

6.07 

1.6 

7.40 

6.97 

6.84 

6.78 

6.75 

6.69 

6.68 

1.7 

8.15 

7.66 

7.50 

7.43 

7.39 

7.33 

7.31 

1.8 

8.93 

8.37 

8.18 

8.09 

8.05 

7.98 

7.96 

1.9 

9.74 

9.11 

8.89 

8.79 

8.74 

8.65 

8.63 

2.0 

10.58 

9.87 

9.62 

9.51 

9.44 

9.34 

9.32 

2.1 

11.44 

10.65 

10.37 

10.24 

10.17 

10.05 

10.02 

2.2 

12.33 

11.46 

11.14 

10.99 

10.91 

10.78 

10.75 

2.3 

13.25 

12.29 

11.93 

11.77 

11.67 

11.52 

11.48 

2.4 

14.20 

13.15 

12.75 

12.56 

12.45 

12.28 

12.24 

2.5 

15.18 

14.03 

13.59 

13.37 

13.25 

13.06 

13.02 

2.6 

16.17 

14.92 

14.44 

14.20 

14.07 

13.85 

13.80 

2.7 

17.19 

15.84 

15.31 

15.05 

14.90 

14.65 

14.60 

2.8 

18.23 

16.79 

16.21 

15.92 

15.76 

15.48 

15.42 

2.9 

19.29 

17.75 

17.12 

16.81 

16.63 

16.32 

16.25 

3.0 

20.38 

18.74 

18.06 

17.71 

17.52 

17.18 

17.10 

3.1 

21.50 

19.74 

19.01 

18.64 

18.42 

18.05 

17.96 

3.2 

22.64 

20.77 

19.98 

19.58 

19.34 

18.93 

18.83 

3.3 

23.80 

21.82 

20.98 

20.54 

20.28 

19.83 

19.72 

3.4 

24.98 

22.89 

21.99 

21.52 

21.24 

20.75 

20.63 

3.5 

26.20 

23.98 

23.01 

22.51 

22.22 

21.69 

21.55 

3.6 

27.42 

25.09 

24.06 

23.52 

23.20 

22.62 

22.48 

3.7 

28.67 

26.23 

25.13 

24.55 

24.21 

23.58 

23.43 

3.8 

29.94 

27.38 

26.22 

25.60 

25.23 

24.56 

24.39 

3.9 

31.23 

28.55 

27.32 

26.66 

26.27  . 

25.54 

25.37 

4.0 

32.54 

29.74 

28.45 

27.74 

27.32 

26.55 

26.35 

4.1 

33.87 

30.96 

29.59 

28.84 

28.39 

27.56 

27.34 

4.2 

35.22 

32.18 

30.75 

29.96 

29.48 

28.59 

28.35 

4.3 

36  ..59 

33.43 

31.92 

31.09 

30.58 

29.63 

29.38 

4.4 

37.99 

34.70 

33.12 

32.24 

31.70 

30.68 

30.42 

*  This  table  should  not  be  used  where  the  weir  is  submerged,  nor  unless  the  overfalling  sheet 
is  aerated  on  the  downstream  face  of  the  weir.  If  a  vacuum  forms  under  the  falling  sheet  the 
discharge  may  be  5  per  cent  greater  than  given  in  this  table. 


190 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  28  (Concluded) 

DISCHARGE  PER  FOOT  OF  LENGTH  OVER  SHARP-CRESTED  VERTICAL   WEIRS 
WITHOUT  END  CONTRACTIONS 


\J 
fc_N 

2 

4 

6 

8 

10 

20 

30 

4.5 

39.40 

35.98 

34.33 

33.40 

32.83 

31.74 

31.47 

4.6 

40.83 

37.29 

35.56 

34.58 

33.98 

32.82 

32.53 

4.7 

42.28 

38.61 

36.80 

35.78 

35.14 

33.92 

33.61 

4.8 

43.75 

39.96 

38.07 

37.00 

36.32 

35.04 

34.70 

4.9 

45.23 

41.32 

39.35 

38.23 

37.52 

36.17 

35.80 

5.0 

46.73 

42.69 

40.65 

39.48 

38.74 

37.21 

36.91 

5.1 

48.25 

44.09 

41.96 

40.73 

39.97 

38.45 

38.03 

5.2 

49.79 

45.50 

43.29 

42.01 

41.20 

39.61 

39.17 

5.3 

51.36 

46.93 

44.64 

43.30 

42.45 

40.78 

40.31 

5.4 

52.94 

48.38 

46.00 

44.60 

43.71 

41.96 

41.47 

5.5 

54.54 

49.85 

47.38 

45.93 

45.00 

43.16 

42.64 

5.6 

56.15 

51.34 

48.79 

47.27 

46.31 

44.38 

43.83 

5.7 

57.78 

52.83 

50.19 

48.62 

47.62 

45.60 

45.02 

5.8 

59.42 

54.34 

51.62 

49.99 

48.94 

46.83 

46.22 

5.9 

61.09 

55.88 

53.07 

51.38 

50.29 

48.08 

47.44 

6.0 

62.77 

57.43 

54.53 

52.78 

51.64 

49.34 

48.67 

6.1 

64.46 

59.00 

56.00 

54.20 

53.02 

50.61 

49.91 

6.2 

66.18 

60.58 

57.50 

55.63 

54.40 

51.90 

51.16 

6.3 

67.91 

62.18 

59.01 

57.07 

55.80 

53.20 

52.42 

6.4 

69.65 

63.79 

60.53 

58.53 

57.22 

54.50 

53.70 

6.5 

71.42 

65.42 

62.07 

60.01 

58.65 

55.82 

54.98 

6.6 

73.19 

67.07 

63.63 

61.50 

60.09 

57.16 

56.27 

6.7 

74.99 

68.74 

65.20 

63.00 

61.55 

58.50 

57.58 

6.8 

76.80 

70.42 

66.78 

64.53 

63.02 

59.96 

58.90 

6.9 

78.62 

72.11 

68.38 

66.06 

64.50 

61.23 

60.22 

7.0 

80.46 

73.82 

70.00 

67.60 

66.00 

62.61 

61.56 

7.1 

82.32 

75.55 

71.63 

69.17 

67.52 

64.00 

62.91 

7.2 

84.18 

77.29 

73.28 

70.74 

69.04 

65.40 

64.27 

7.3 

86.07 

79.04 

74.94 

72.34 

70.58 

66.81 

65.64 

7.4 

87.97 

80.81 

76.61 

73.94 

72.14 

68.24 

67.02 

7.5 

89.89 

82.60 

78.30 

75.56 

73.70 

69.68 

68.41 

7.6 

91.82 

84.40 

80.01 

77.19 

75.28 

71.13 

69.81 

7.7 

93.76 

86.22 

81.73 

78.84 

76.88 

72.59 

71.23 

7.8 

95.72 

88.05 

83.46 

80.50 

78.48 

74.06 

72.65 

7.9 

97.70 

89.90 

85.21 

82.18 

80.11 

75.55 

74.09 

8.0 

99.68 

91.75 

86.97 

83.87 

81.74 

77.04 

75.53 

8.1 

101.69 

93.63 

88.75 

85.57 

83.39 

78.55 

76.98 

8.2 

103.70 

95.51 

90.54 

87.29 

85.25 

80.06 

78.44 

8.3 

105.73 

97.42 

92.34 

89.02 

86.72 

81.59 

79.92 

8.4 

107.78 

99.34 

94.16 

90.76 

88.41 

83.13 

81.40 

8.5 

109.84 

101.27 

96.00 

92.52 

90.11 

84.69 

82.90 

8.6 

111.91 

103.21 

97.84 

94.29 

91.82 

86.25 

84.41 

8.7 

113.99 

105.17 

99.70 

96.07 

93.55 

87.82 

85.92 

8.8 

116.09 

107.14 

101.57 

97.87 

95.28 

89.40 

87.44 

8.9 

118.20 

109.13 

103.46 

99.68 

97.04 

91.00 

88.98 

9.0 

120.33 

111.13 

105.36 

101.50 

98.80 

92.61 

90.52 

9.1 

122.47 

113.15 

107.28 

103.34 

100.58 

94.23 

92.08 

9.2 

124.62 

115.18 

109.21 

105.19 

102.37 

95.86 

93.65 

9.3 

126.79 

117.22 

111.15 

107.06 

104.17 

97.49 

95.22 

9.4 

128.97 

119.27 

113.10 

108.93 

105.99 

99.14 

96.80 

9.5 

131.16 

121.34 

115.07 

110.82 

107.82 

100.80 

98.40 

9.6 

133.36 

123.42 

117.05 

112.72 

109.65 

102.48 

100.00 

9.7 

135  .  58 

125.51 

119.04 

114.64 

111.50 

104.16 

101.62 

9.8 

137.82 

127.63 

121.05 

116.57 

113.37 

105.85 

103.25 

9.9 

140.06 

129.74 

123.07 

118.51 

115.25 

107.56 

104.88 

10.0 

142.31 

131.87 

125.10 

120.46 

117.14  |    109.27 

106.52 

HYDRAULIC   DIAGRAMS   AND   TABLES 


191 


Tables  28A,  28B,  and  28C  give  multipliers  to  be  applied 
to  quantities  in  Table  28  to  determine  the  discharge  over  broad- 
crested  weirs  of  various  types  and  dimensions.  Example:  Sup- 


pose  the  discharge  is  to  be  computed  over  a  rectangular  weir 
that  is  10  feet  long,  12  feet  high,  6  feet  crest  width,  and  has  an 
observed  head  of  2.4  feet.  Table  28  shows  that  for  a  height  (p) 
of  12  feet  and  a  head  (ti)  of  2.4,  the  discharge  is  12.42  second- 
feet.  Table  28A  shows  that  for  a  height  (p)  of  12  feet,  a  crest 
width  (c)  of  6  feet,  and  head  (ti)  of  2.4  feet  the  multiplier  is 
0.797.  Hence,  the  discharge  is  12.42  X  0.797  X  10  =  99.0 
second-feet. 


192 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


TABLE  28A 

MULTIPLIERS  OF  DISCHARGE  OVER  RECTANGULAR  WEIR,  BROAD-CRESTED 
(TYPE  a,  SEE  FIGURE) 

[p  =  height  of  weir;  c  =  width  of  crest;  h  =  observed  head;  all  in  feet] 


P 

c 

4.6 
2.6 

4.6 
6.6 

11.25 
.48 

11.25 
.93 

11.25 
1.65 

11.25 
3.17 

11.25 
5.88 

11.25 
8.98 

11.25 
12.24 

11.25 
16.30 

h 

0.5 

.821 

.792 

.806 

.792 

.799 

.801 

.786 

.790 

1.0 

'.765 

!708 

.997 

.899 

.808 

.795 

.791 

.794 

.815 

.790 

1.5 

.789 

.709 

1.00 

.982 

.878 

.796 

.796 

.793 

.814 

.792 

2.0 

.814 

.710 

1.00 

.00 

.906 

.815 

.797 

.792 

.797 

.793 

2.5 

.835 

.711 

1.00 

.00 

.985 

.844 

.797 

.790 

.796 

.793 

3.0 

.857 

.711 

1.00 

.00 

1.00 

.870 

.797 

.788 

.794 

.791 

3.5 

.878 

.712 

1.00 

.00 

.00 

.90 

.812 

.787 

.794 

.791 

4.0 

.899 

.714 

1.00 

.00 

.00 

.93 

.834 

.786 

.792 

.789 

5.0 

.940 

.716 

1.00 

.00 

.00 

.97 

(a) 

.78 

.79 

.78 

6.0 

.986 

.718 

1.00 

.00 

.00 

.98 

(a) 

.78 

.78 

.78 

7.0 

1.00 

.00 

.00 

(a) 

(a) 

.77 

.78 

.77 

8.0 

1.00 

.00 

.00 

(a) 

(a) 

.77 

.77 

.77 

9.0 

1.00 

.00 

.00 

(a) 

(a) 

.77 

.77 

.77 

10.0 

1.00 

.00 

1.00 

(a) 

(a) 

.77 

.77 

.77 

(a)  Value  doubtful. 


TABLE  28B 
MULTIPLIERS  OF  DISCHARGE  FOR  TRAPEZOIDAL  WEIRS 

[p  =  height  of  weir,  in  feet;  c  =  width  of  crest,  in  feet;  s  =  upstream  slope; 
s'  =  downstream  slope;  h  =  observed  head,  in  feet] 


Type  b  (see  Figure) 

(see  Figure) 

P 

c 
s 
s' 

4.9 
.33 
2:1 
0 

4.9 
.66 
2:1 
0 

4.9 
.66 
3:1 
0 

4.9 
.66 
4:1 
0 

4.9 
.66 
5:1 
0 

4.9 
.33 
2:1 
5:1 

4.9 
.66 
2:1 
2:1 

4.65 
7.00 
4.67:1 

11.25 
6.00 
6:1 

h 
1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 
5.0 
6.0 
7.0 
8.0 
9.0 
10.0 

.137 
.131 
.120 

.106 
.094 
.085 
.072 
.064 

1.048 
1.068 
1.080 
1.085 
1.088 
1.087 
1.084 
1.081 

.066 

.066 
.061 
.052 
.047 
.043 
.038 
.035 

1.039 

1.039 
1.033 
1.026 
1.020 
1.017 
1.012 
1.009 

1.009 
1.009 
1.005 
.997 
.991 
.988 
.984 
.980 

1.095 

1.071 
1.044 
1.024 
1.009 
1.003 
1.014 
1.023 

.071 

.066 
.053 
.047 
.047 
1.050 
1.052 
1.055 

1.042 
1.033 
1.024 
1.012 
.995 
.983 
.977 
.974 
.97 
.97 
.97 
.96 
.96 
.96 

1.060 

1.069 
1.054 
1.012 
.985 
.979 
.976 
.973 
.97 
.96 
.96 
.95 
.95 
.95 

HYDRAULIC  DIAGRAMS  AND   TABLES 

TABLE  28C 

MULTIPLIERS  OF  DISCHARGE  FOR  COMPOUND  WEIRS 
[p  =  height  of  weir,  in  feet;  h  =  observed  head,  in  feet] 


193 


p 

4.57 

4.56 

4.53 

5.28 

11.25 

11.25 

11.25 

11.25 

11.25 

11.25 

Type 
(see 
Figure) 

d  • 

- 

/ 

g 

h 

i 

J 

k 

/ 

m 

h 
0  5 

.941 

.924 

.933 

.962 

.971 

.947 

1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
5.0 
6.0 

.842 
.866 
.888 
.906 
.927 
.945 
.965 
1.00 

.836 
.834 
.831 
.826 
.822 
.817 
.812 
.80 

.929 
.950 
.953 
.947 
.942 
.936 
.931 
.92 

.976 
.979 
.988 
1.000 
1.016 
1.032 
1.044 
1.05 

1.039 
1.087 
1.109 
1.118 
1.120 
1.127 
.123 
.11 
.11 

.033 
.093 
.133 
.153 
.163 
.169 
.165 
1.16 
1.15 

.988 
1.018 
1.033 
1.045 
1.054 
1.060 
1.060 
1.05 
1.04 

1.045 
1.066 
1.063 
1.020 
.997 
.994 
.991 
.98 
.98 

1.033 
1.042 
1.035 
1.033 
1.045 
1.054 
1.057 
1.05 
1.04 

.000 
.036 
.063 
.085 
.096 
.108 
.110 
.10 
.10 

7.0 

.10 

1.14 

1.04 

.97 

1.04 

.09 

8.0 

.10 

1.14 

1.04 

.97 

1.03 

.09 

9.0 

.09 

1.14 

1.03 

.97 

1.03 

.08 

10.0 

.09 

1.13 

1.03 

.97 

1.03 

1.08 

194 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  29 

ACRE-FEET  EQUIVALENT  TO  A  GIVEN  NUMBER  OF  SECOND-FEET  FLOWING 
FOR  A  GIVEN  LENGTH  OF  TIME 


Second- 
Feet 

DAYS  OF  24  HOURS 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0.01 

0.0198 

.0396 

0.0595 

.0793 

.0991 

.1190 

.1388 

.1586 

.1785 

.1983 

.02 

.0396 

.0793 

.1190 

.1586 

.1983 

.2380 

.2776 

.3173 

.3570 

.3966 

.03 

.0595 

.1190 

.1785 

.2380 

.2975 

.3570 

.4165 

.4760 

.5355 

.5950 

.04 

.0793 

.1586 

.2380 

.3173 

.3966 

.4760 

.5553 

.6347 

.7140 

.7933 

.05 

.0991 

.1983 

.2975 

.3966 

.4958 

.5950 

.6942 

.7933 

.8925 

.9917 

.06 

.1190 

.2380 

.3570 

.4760 

.5950 

.7140 

.8330 

.9520 

1.071 

1.190 

.07 

.1388 

.2776 

.4165 

.5553 

.6942 

.8330 

.9719 

1.110 

1.249 

1.388 

.08 

.1586 

.3173 

.4760 

.6347 

.7933 

.9520 

1.110 

1.269 

1.428 

1.586 

.09 

.1785 

.3570 

.5355 

.7140 

.8925 

1.071 

1.249 

1.428 

1.606 

1.785 

.10 

.1983 

.3966 

.5950 

.7933 

.9917 

1.190 

1.388 

1.586 

1.785 

1.983 

.11 

.2181 

.4363 

.6545 

.8727 

1.090 

1.309 

1.527 

1.745 

1.963 

2.181 

.12 

.2380 

.4760 

.7140 

.9520 

1.190 

1.428 

1.666 

1.904 

2.142 

2.380 

.13 

.2578 

.5157 

.7735 

1.031 

1.289 

1.547 

1.804 

2.022 

2.320 

2.578 

.14 

.2776 

.5553 

.8330 

1.110 

1.388 

1.666 

1.943 

2.221 

2.499 

2.776 

.15 

.2975 

.5950 

.8925 

1.190 

1.487 

1.785 

2.082 

2.380 

2.677 

2.975 

.16 

.3173 

.6347 

.9520 

1.269 

1.586 

1.904 

2.221 

2.538 

2.856 

3.173 

.17 

.3371 

.6743 

1.011 

1.348 

1.685 

2.023 

2.360 

2.697 

2.034 

3.371 

.18 

.3570 

.7140 

1.071 

1.428 

1.785 

2.142 

2.499 

2.856 

3.213 

3.570 

.19 

.3768 

.7537 

1.130 

1.507 

1.884 

2.261 

2.638 

3.014 

3.391 

3.768 

.20 

.3966 

.7933 

1.190 

1.586 

1.983 

2.380 

2.776 

3.173 

3.570 

3.966 

.21 

.4165 

.8330 

1.249 

1.666 

2.082 

2.499 

2.915 

3.332 

3.748 

4.165 

.22 

.4363 

.8727 

1.309 

1.745 

2.181 

2.618 

3.054 

3.490 

3.927 

4.363 

.23 

.4562 

.9124 

1.368 

1.824 

2.280 

2.737 

3.193 

3.649 

4.105 

4.561 

.24 

.4760 

.9520 

1.428 

1.904 

2.380 

2.856 

3.332 

3.808 

4.284 

4.760 

.25 

.4958 

.9917 

1.487 

1.983 

2.479 

2.975 

3.471 

3.966 

4.462 

4.958 

.26 

.5157 

1.031 

1.547 

2.062 

2.578 

3.094 

3.609 

4.125 

4.641 

5.157 

.27 

.5355 

1.071 

1.606 

2.142 

2.677 

3.213 

3.748 

4.284 

4.819 

5.355 

.28 

.5553 

1.110 

1.666 

2.221 

2.776 

3.332 

3.887 

4.442 

4.998 

5.553 

.29 

.5752 

1.150 

1.725 

2.300 

2.876 

3.451 

4.026 

4.601 

5.176 

5.752 

.30 

.5950 

1.190 

1.785 

2.380 

2.975 

3.570 

4.165 

4.760 

5.355 

5.950 

.31 

.6148 

1.229 

1.844 

2.459 

3.074 

3.689 

4.304 

4.919 

5.533 

6.148 

.32 

.6347 

1.269 

1.904 

2.538 

3.173 

3.808 

4.442 

5.077 

5.712 

6.347 

.33 

.6545 

1.309 

1.963 

2.618 

3.272 

3.927 

4.581 

5:236 

5.890 

6.545 

.34 

.6743 

1.348 

2.023 

2.697 

3.371 

4.046 

4.720 

5.395 

6.069 

6.743 

.35 

.6942 

1.388 

2.082 

2.776 

3.471 

4.165 

4.859 

5.553 

6.247 

6.942 

.36 

.7140 

1.428 

2.142 

2.856 

3.570 

4.284 

4.998 

5.712 

6.426 

7.140 

.37 

.7338 

1.467 

2.201 

2.935 

3.669 

4.403 

5.137 

5.871 

6.604 

7.338 

.38 

.7537 

1.507 

2.261 

3.014 

3.768 

4.522 

5.276 

6.029 

6.783 

7.537 

.39 

.7735 

1.547 

2.320 

3.094 

3.867 

4.641 

5.414 

6.188 

6.961 

7.735 

.40 

.7933 

1.586 

2.380 

3.173 

3.966 

4.760 

5.553 

6.347 

7.140 

7.933 

.41 

.8132 

1.626 

2.439 

3.252 

4.066 

4.879 

5.692 

6.505 

7.319 

8.132 

.42 

.8330 

1.666 

2.499 

3.332 

4.165 

4.998 

5.831 

6.664 

7.497 

8.330 

.43 

.8528 

1.705 

2.558 

3.411 

4.264 

5.117 

5.970 

6.823 

7.676 

8.528 

.44 

.8727 

1.745 

2.618 

3.490 

4.363 

5.236 

6.109 

6.981 

7.854 

8.727 

.45 

.8925 

1.785 

2.677 

3.570 

4.462 

5.355 

6.247 

7.140 

8.033 

8.925 

.46 

.9124 

1.824 

2.737 

3.649 

4.561 

5.474 

6.386 

7.299 

8.211 

9.123 

.47 

.9322 

1.864 

2.796 

3.728 

4.661 

5.593 

6.525 

7.457 

8.390 

9.322 

.48 

.9520 

1.904 

2.856 

3.808 

4.760 

5.712 

6.664 

7.616 

8.568 

9.520 

.49 

.9719 

1.943 

2.915 

3.887 

4.859 

5.831 

6.803 

7.775 

8.747 

9.719 

0.50 

0.9917 

1.983 

2.975 

3.966 

4.958 

5.950 

6.942 

7.933 

8.925 

9.917 

NOTE. — For  larger  quantities  and  greater  number  of  days  than  given  in 
this  table  it  is  only  necessary  to  move  the  decimal  point,  thus,  for  .25  c.  f.  s. 
flowing  six  days  we  read  the  equivalent  2.975  acre-feet  and  for  25  c.  f.  s.  the 
equivalent  in  acre -feet  is  297.5.  Again,  .25  c.  f.  s.  flowing  sixty  days  =  29.75 
acre-feet  and  25  c.  f.  s.  flowing  sixty  days  =  2975  acre-feet,  etc.,  etc. 


HYDRAULIC   DIAGRAMS   AND   TABLES 


195 


TABLE   29  (Concluded) 

ACRE-FEET  EQUIVALENT  TO  A  GIVEN  NUMBER  OF  SECOND-FEET  FLOWING 
FOR  A  GIVEN  LENGTH  OF  TIME 


Second- 
Feet 

DAYS  OF  24  HOURS 

1             2 

3 

4 

5 

6 

7 

8 

9 

10 

0.51 

1.011      2.023 

3.034 

4.046 

5.057 

6.069 

7.080 

8.092 

9.104 

10.115 

.52 

1.031 

2.062 

3.094 

4.125 

5.157 

6.188 

7.219 

8.251 

9.282 

10.314 

.53 

1.051 

2.102 

3.153 

4.204 

5.256 

6.307 

7.358 

8.409 

9.461 

10.519 

.54 

1.071 

2.142 

3.213 

4.284 

5.355 

6.426 

7.497 

8.568 

9.639 

10.710 

.55 

1.090 

2.181 

3.272 

4.363 

5.454 

6.545 

7.636 

8.727 

9.818 

10.909 

.56 

1.110 

2.221 

3.332 

4.442 

5.553 

6.664 

7.775 

8.885 

9.996 

11.107 

.57 

1.130 

2.261 

3.391 

4.522 

5.652 

6.783 

7.914 

9.044 

10.175 

11.305 

.58 

1.150 

2.300 

3.451 

4.601 

5.752 

6.902 

8.052 

9.203 

10.353 

11.504 

.59 

1.170 

2.340 

3.510 

4.680 

5.851 

7.021 

8.191 

9.361 

10.532 

11.702 

.60 

1.190 

2.380 

3.570 

4.760 

5.950 

7.140 

8.330 

9.520 

10.710 

11.900 

.61 

1.209 

2.419 

3.629 

4.839 

6.049 

7.259 

8.469 

9.679 

10.889 

12.099 

.62 

1.229 

2.459 

3.689 

4.919 

6.148 

7.378 

8.608 

9.838 

11.067 

12.297 

.63 

1.249 

2.499 

3.748 

4.998 

6.247 

7.497 

8.747 

9.996 

11.246 

12.495 

.64 

1.269 

2.538 

3.808 

5.077 

6.347 

7.616 

8.885 

10.155 

11.424 

12.694 

.65 

1.289 

2.578 

3.867 

5.157 

6.446 

7.735 

9.024 

10.314 

11.603 

12.892 

.66 

1.309 

2.618 

3.927 

5.236 

6.545 

7.854 

9.163 

10.472 

11.781 

13.090 

.67 

1.328 

2.657 

3.986 

5.315 

6.644 

7.973 

9.302 

10.631 

11.960 

13.289 

.68 

1.348 

2.697 

4.046 

5.395 

6.743 

8.092 

9.441 

10.790 

12.138 

13.487 

.69 

1.368 

2.737 

4.105 

5.474 

6.842 

8.211 

9.580 

10.948 

12.317 

13.685 

.70 

1.388 

2.776 

4.165 

5.553 

6.942 

8.330 

9.719 

11.107 

12.495 

13.884 

.71 

1.408 

2.816 

4.224 

5.633 

7.041 

8.449 

9.857 

11.266 

12.674 

14.082 

.72 

1.428 

2.856 

4.284 

5.712 

7.140 

8.568 

9.996 

11.424 

12.852 

14.280 

.73 

1.447 

2.895 

4.343 

5.791 

7.239 

8.687 

10.135 

11.583 

13.031 

14.479 

.74 

1.467 

2.935 

4.403 

5.871 

7.338 

8.806 

10.274 

11.742 

13.209 

14.677 

.75 

1.487 

2.975 

4.462 

5.950 

7.438 

8.925 

10.413 

11.900 

13.388 

14.876 

.76 

1.507 

3.014 

4.522 

6.029 

7.537 

9.044 

10.552 

12.059 

13.566 

15.074 

.77 

1.527 

3.054 

4.581 

6.109 

7.636 

9.163 

10.690 

12.218 

13.745 

15.272 

.78 

1.547 

3.094 

4.641 

6.188 

7.735 

9.282 

10.829 

12.376 

13.923 

15.471 

.79 

1.566 

3.133 

4.700 

6.267 

7.834 

9.401 

10.968 

12.535 

14.102 

15.669 

.80 

1.586 

3.173 

4.760 

6.347 

7.933 

9.520 

11.107 

12.694 

14.280 

15.867 

.81 

1.606 

3.213 

4.819 

6.426 

8.033 

9.639 

11.246 

12.852 

14.459 

16.066 

.82 

1.626 

3.252 

4.879 

6.505 

8.132 

9.758 

11.385 

13.011 

14.638 

16.264 

.83 

1.646 

3.292 

4.938 

6.585 

8.231 

9.877 

11.523 

13.170 

14.816 

16.462 

.84 

1.666 

3.332 

4.998 

6.664 

8.330 

9.996 

11.662 

13.328 

14.995 

16.661 

.85 

1.685 

3.371 

5.057 

6.743 

8.429 

10.115 

11.801 

13.487 

15.173 

16.859 

.86 

1.705 

3.411 

5.117 

6.823 

8.528 

10.234 

11.940 

13.646 

15.352 

17.057 

.87 

1.725 

3.451 

5.176 

6.902 

8.628 

10.353 

12.079 

13.804 

15.530 

17.256 

.88 

1.745 

3.490 

5.236 

6.981 

8.727 

10.472 

12.218 

13.963 

15.709 

17.454 

.89 

1.765 

3.530 

5.295 

7.061 

8.826 

10.591 

12.357 

14.122 

15.887 

17.652 

.90 

1.785 

3.570 

5.355 

7.140 

8.925 

10.710 

12.495 

14.280 

16.066 

17.851 

.91 

1.804 

3.609 

5.414 

7.219 

9.024 

10.829 

12.634 

14.439 

16.244 

18.049 

.92 

1.824 

3.649 

5.474 

7.299 

9.123 

10.948 

12.773 

14.598 

16.423 

18.247 

.93 

1.844 

3.689 

5.533 

7.378 

9.223 

11.067 

12.912 

14.757 

16.601 

18.446 

.94 

.864 

3.728 

5.593 

7.457 

9.322 

11.186 

13.051 

14.915 

16.780 

18.644 

.95 

.884 

3.768 

5.652 

7.537 

9.421 

11.305 

13.190 

15.074 

16.958 

18.842 

.96 

.904 

3.808 

5.712 

7.616 

9.520 

11.424 

13.328 

15.233 

17.137 

19.041 

.97 

.923 

3.847 

5.771 

7.695 

9.619 

11.543 

13.467 

15.391 

17.315 

19.239 

.98 

.943 

3.887 

5.831 

7.775 

9.719 

11.662 

13.606 

15.550 

17.494 

19.438 

.99 

1.963 

3.927 

5.890 

7.854 

9.818 

11.781 

13.745 

15.709 

17.672 

19.636 

1.00 

1.983 

3.966 

5.950 

7.933 

9.917 

11.900 

13.884 

15.867 

17.851 

19.834 

196 


WORKING   DATA   FOR  IRRIGATION   ENGINEERS 


Water  Duty 


300 


1 


| 

*P» 

9 

.2 

I 

g  m 


P 

I" 

Z   70 


g 


35 


30 


40 


< 


/ 


• 


/ 


50  60  70          80         90       100  150 

A  =  Area  in  Acres  Supplied  by  One  Second  Foot 


200 


FIG.  38. — Diagram  for  Converting     "Acres  per  Second-foot"  to  "Depth  of 

1  9835  ^V 
Water  Applied  in  Given  Length  of  Time,"    W  =  -L—^ — 


HYDRAULIC  DIAGRAMS   AND   TABLES 


197 


*1 
'  ' 

I 

0    M   3         g       "!"§3."oJpg'Og»g   ^   §  .§ 

.,;' 

iilljl  ^ll!|;  1  |l1'«1l§ 

•^  <1                                                C)<ltL|                          ^  O          fc 

1                 |          P                         |                    | 

^)                                  *^                             ^H                                                  Q                                           O 

en 

"cS                            ^                B'~$                                      ***                                S 

i 

S 

*o           ^                           C  c                                *S                             ^ 

0       J5        c          S-S                                            *o 

Pi 

o 

gfc 

1 

3 

p 

•^    £   £     so            •:          It 

3  = 

ttJ 

*s      *i     ^^     ^^^                                '   | 
•    >      2  2     "^  ""S                                 "o-0 

PQ  £ 

"cS'cS'S^S^^                            "^                                   w 

<  P 
H  S 

§ 

llllJlJl      11     p 

H       H       ffi          J                           >                    Q 

g 

1 

B 

Ht 

i 

>    s. 

(N 

o        10 

°°          i2                                                                                                      -s* 

11      ®   K:                             !•§,              <N 

^        r  a*                 "^         "^ 

H          II          II             II                                H                        H 

iN' 

r-i            C^           CO               -^                                            1C                                CD 

198 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


f 


TABLE  Continued) 
LIST  OF  HYDRAULIC  FORMUL 


30—  ( 


ou 

ii  ! 


ttj 


as 


S5S    |g      S 


co      CO<N      ^          co 

II    II 


00  Oi 


+  > 

II  II 

fcj  H^ 

ic  «o 


HYDRAULIC  DIAGRAMS  AND  TABLES 


199 


«*;       -r)  <l>  0)  0) 


gt. 

•SO 


S  a 


^ra  W»a  5 

8SH| 

<£j  0.2  ^  6 

QJ    C2    ^^* 
rj   4J    G    "»w 

^  c  S  ^ 

^)    QJ    C 
V4-i    (j    U<    G    fl.) 

«?^i  rt  rt*> 


Hi 

O  esS 


II  II 


K  H5 


1 

U 


|  _ 


u. 
.  o 


:>       u. 


^cn  o  ^cn  to  .«  a.tn  ^  ro 

"in     P  ">-i     tti  "in     D  ">-i  •  r-i  "^ 

o^ooo-go^0 


+ 


^          H 


O» 


Kl 


O5          O          i-H 


200  WORKING  DATA   FOR   IRRIGATION   ENGINEERS 


CHAPTER  V 

STRUCTURAL  DIAGRAMS 
AND  TABLES 


CHAPTER  V 

STRUCTURAL   DIAGRAMS  AND  TABLES 

Fig.  39  gives  the  volume  of  excavation  and  embankment  in 
cubic  yards  per  100  feet  for  small  canals  in  ground  which  is 
level  transversely.  In  deriving  the  equations  for  volume  of 
embankment  two  cases  must  be  considered:  Case  I,  where  the 
bed  of  canal  is  below  the  ground  surface;  and  Case  II,  where 


Ground  Surface 


"//WyvvW'Mvy 
Case  II 


TYPICAL  SECTIONS 


the  bed  of  canal  is  above  the  ground  surface.     The  two  cases 
are  illustrated  in  the  accompanying  figure. 

Case  I.— 

Equations:  Cut    V  =  3.7  (b  c  +  1.5  c2),  in  cubic  yds.  per  100  ft. 

Fill     F!  =  7.4  [a(d  +  h-c)  +  l.5(d  +  h-  c)2] 

Example:  Assume  6  =  3 
c  =  2 


Enter  the  diagram  with  these  arguments  and  read  directly — 
cut  V  =  44  cubic  yards.  To  get  the  "  fill,"  enter  the  diagram 
at  c  =  2,  follow  the  diagonal  line  from  this  point  to  its  intersec- 
tion with  the  vertical  line  marked  d  +  h  =  3 ;  thence  horizontally 
to  the  right  to  the  curve  marked  "a  =  2  "  and  read  on  the 
upper  scale  Vi  =  26.  The  cut  in  this  case  exceeds  the  fill,  and 
the  former  is,  therefore,  the  controlling  factor.  For  a  cut  c  of  1 
foot  the  excavation  is  found  to  be  13  cubic  yards  and  the  fill  73 

203 


204  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

cubic  yards.  In  this  case  the  fill  is  the  controlling  factor,  as  it 
exceeds  the  cut  by  60  cubic  yards. 

Case  II.  —  In  this  case  the  canal  is  entirely  in  fill,  and  two 
quantities  jnust  be  looked  out  from  the  diagram  to  make  up  the 
total  fill.  In  calculating  fills,  the  simplest  process  is  to  calculate 
the  sum  of  the  two  embankments  considered  as  full  trapezoidal 
sections  with  bases'"  a"  Referring  to  the  diagram,  it  will  be 
seen  that  for  the  condition  there  represented  as  "  Case  II,"  we 
must  deduct  from  the  total  quantity  thus  obtained  the  volume 
of  the  lower  shaded  triangular  prism,  and  add  the  volume  of  the 
upper  shaded  triangular  prism.  The  algebraic  sum  of  these  two 
triangular  prisms  may  be  either  positive,  negative,  or  zero, 
depending  upon  whether  the  upper  prism  is  greater  than,  less 
than,  or  equal  to  the  lower  prism.  The  general  equation  for 

this  sum  is  E  =  -  .617  [(3  d  -  b)2  -  62J.    The  plot  of  this 

equation  on  the  diagram  shows  the  positive  values  of  E  on  the 
left  of  the  vertical  axis,  negative  values  on  the  right,  and  zero 
values  at  the  intersection  of  curves  with  the  vertical  axis.  The 
complete  equation  for  embankment  in  Case  II  is: 

Total  volume 
=  Fi  +  E  =  7.4  [a  (d  +  h  +  a)  +  l.5(d  +  h  +  Ci)2]  -0.617  [(3  ci-6)2  -62 

Example:     Assume  b  =  2 


To  get  FI,  enter  the  diagram  at  c\  =  2  or  c  =  —  2;  thence 
follow  the  diagonal  line  to  d  +  h  =  2;  thence  horizontally  to  the 
right  to  the  curve  marked  a  =  2  and  read  on  the  lower  scale 
Fi  =  237  c.y.  Now  to  get  E,  enter  the  diagram  at  the  same 
point,  Ci  =  2;  thence  horizontally  to  the  right  to  the  curve 
for  E  marked  b  =  2  and  read  —  8  c.y.  The  net  fill,  then,  is 
Fi  +  E  =  237  -  8  =  229  c.y. 

If  b  =  3  and  the  other  factors  remain  the  same,  E  =  zero, 
and  if  b  =  3.5,  E  =  +  4,  the  value  of  Fi  remaining  the  same 
in  all  three  cases,  as  it  is  independent  of  the  bottom  width  of 
canal. 


STRUCTURAL  DIAGRAMS  AND   TABLES 


205 


FIG.  39. — Volume  of  Excavation  and  Embankment  for  Small  Canals 
in  Level  Gu  Jid. 


206  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

The  object  of  using  two  different  scales  for  the  values  of  Vi 
is  merely  to  shorten  up  the  diagram,  the  lower  set  of  curves  for 
Vi  being  a  continuation  of  the  four  upper  curves,  and  the  lower 
scale  a  continuation  of  the  upper.  Fig.  39  illustrates  a  simple 
and  rapid  means  of  calculating  embankment  quantities  on  level 
ground.  This  particular  diagram  is  offered  principally  as  an 
illustration  of  the  manner  of  plotting  the  equations,  rather 
than  for  practical  usefulness,  although  it  may  be  considered 
fairly  accurate  for  the  range  of  values  of  the  various  factors 
that  it  covers.  It  will  be  found,  however,  that  for  continuous 
use  such  a  scale  is  rather  hard  on  the  eyes,  and  larger  scales 
are  desirable,  which  for  obvious  reasons  are  not  used  here. 

Tables  31  to  34  give  the  volume  of  excavation  in  cubic  yards 
per  100  feet  of  length  for  various  center  depths  and  side  slopes, 
assuming  the  ground  to  be  level  transversely.  The  volume 
required  is  the  difference  between  two  triangular  prisms. 

In  the  figure  below  is  shown  the  cross-section  of  a  canal  that 
has  a  bottom  width  of  18  feet  and  side  slopes  of  l|  to  1.  The 


amount  of  material  in  the  prism  C  B  F  E  is  equal  to  the  volume 
of  the  prism  ACE  minus  the  volume  of  the  prism  A  B  F. 
As  A  C  E  has  an  altitude  of  16  feet  and  A  B  F  has  an  altitude  of 
6  feet,  the  volume  of  each  for  a  length  of  100  feet  can  be  obtained 
from  the  table.  Opposite  16  in  Table  32  is  1,422,  which  is  the 
volume  in  cubic  feet  of  A  C  E  per  100  linear  feet;  opposite  6  is 
200,  which  is  the  volume  of  A  B  F. 

As  C  BF  E  =  AC  E-  A  B  F 

C  BF  E  =  1,422-  200 

=  1,222  cubic  yards 

When  working  up  quantities  for  canal  excavation  the  volume 
of  A  B  F  need  not  be  subtracted  at  each  station,  but  need 


STRUCTURAL  DIAGRAMS  AND   TABLES  207 

be  subtracted  only  when  a  change  of  canal  section  or  classifica- 
tion of  material  occurs.  When  this  is  done,  it  is  obvious  that  the 
volume  to  be  subtracted  is  the  volume  of  A  B  F  per  100-foot 
station  multiplied  by  the  number  of  stations  covered.  No  inter- 
polation is  necessary,  as  the  cuts  are  never  measured  closer 
than  the  nearest  0.1  foot. 

Tables  35  to  37  give  the  volume  of  excavation  in  cubic  yards 
per  100  feet  of  length,  where  the  surface  slopes  transversely,  for 
various  center  depths  and  side  slopes.  They  differ  from  Tables 
31  to  34  only  in  that  the  earth  surface  is  sloping  ground  instead 
of  being  level  transversely.  The  surface  slope  is  expressed  in 
per  cent,  a  10  per  cent  slope  being  10  vertical  to  100  horizontal. 


In  the  above  figure  is  shown  a  section  of  canal  in  sloping 
ground.  The  depth  of  center  cut  to  A  is  18  feet;  entering  Table 
36,  with  a  depth  of  18,  we  read  the  volume  of  C  A  E  =  1841. 
The  volume  of  B  A  F  is  always  read  from  the  tables  for  level 
cut;  this  volume  is  found  in  Table  32  to  be  200  cubic  yards. 
The  volume  of  the  canal  prism  per  100  feet  is,  therefore, 

C  A  E-  BAF  =  1841  -  200  =  1641  cubic  yards. 

When  working  up  quantities  for  canal  excavation,  the  volume 
of  B  A  F  need  not  be  subtracted  at  each  station,  but  need  be 
subtracted  only  when  a  change  of  canal  section  or  classification  of 
material  occurs.  When  this  is  done,  it  is  obvious  that  the  volume 
to  be  subtracted  is  the  volume  of  B  A  F  per  100-foot  station 
multiplied  by  the  number  of  stations  covered. 


208 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  31 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  LEVEL  CUT 
Side  Slopes  1  to  1 


Depth  of  || 

Center  Cut, 
in  Feet 

0. 

l. 

2." 

3. 

4. 

5. 

6. 

.7 

.8 

.9 

0 

0.0 

0.0 

0.1 

0.3 

0.6 

0.9 

1.3 

1.8 

2.4 

3.0 

1 

3.7 

4.5 

5.3 

6.3 

7.3 

8.3 

9.5 

10.7 

12.0 

13.4 

2 

15 

16 

18 

20 

21 

23 

25 

27 

29 

31 

3 

33 

36 

38 

40 

43 

45 

48 

51 

54 

56 

4 

59 

62 

65 

68 

72 

75 

78 

82 

85 

89 

5 

93 

96 

100 

104 

108 

112 

116 

120 

125 

129 

6 

133 

138 

142 

147 

152 

156 

161 

166 

171 

176 

7 

181 

187 

192 

197 

203 

208 

214 

220 

225 

231 

8 

237 

243 

249 

255 

261 

268 

274 

280 

287 

293 

9 

300 

307 

313 

320 

327 

334 

341 

349 

356 

363 

10 

370 

378 

385 

393 

401 

408 

416 

424 

432 

440 

11 

448 

456 

465 

473 

481 

490 

498 

507 

516 

524 

12 

533 

542 

551 

560 

569 

579 

588 

597 

607 

616 

13 

626 

636 

645 

655 

665 

675 

685 

695 

705 

716 

14 

726 

736 

747 

757 

768 

779 

789 

800 

811 

822 

15 

833 

844 

856 

867 

878 

890 

901 

913 

925 

936 

16 

948 

960 

972 

984 

996 

,008 

1,021 

1,033 

,045 

1,058 

17 

,070 

1,083 

,096 

1,108 

,121 

,134 

,147 

1,160 

,173 

,187 

18 

,200 

1,213 

,227 

1,240 

,254 

,268 

,281 

1,295 

,309 

,323 

19 

,337 

,351 

,365 

1,380 

,394 

,408 

,423 

1,437 

,452 

,467 

20 

,481 

,496 

,511 

1,526 

,541 

,556 

,572 

1,587 

,602 

,618 

21 

,633 

,649 

,665 

1,680 

,696 

,712 

,728 

1,744 

,760 

,776 

22 

1,793 

,809 

,825 

1,842 

1,858 

,875 

1,892 

1,908 

1,925 

,942 

23 

1,959 

,976 

1,993 

2,011 

2,028 

2,045 

2,063 

2,080 

2,098 

2,116 

24 

2,133 

2,151 

2,169 

2,187 

2,205 

2,223 

2,241 

2,260 

2,278 

2,296 

25 

2,315 

2,333 

2,352 

2,371 

2,389 

2,408 

2,427 

2,446 

2,465 

2,484 

26 

2,504 

2,523 

2,542 

2,562 

2,581 

2,601 

2,621 

2,640 

2,660 

2,680 

27 

2,700 

2,720 

2,740 

2,760 

2,781 

2,801 

2,821 

2,842 

2,862 

2,883 

28 

2,904 

2,924 

2,945 

2,966 

2,987 

3,008 

3,029 

3,051 

3,072 

3,093 

29 

3,115 

3,136 

3,158 

3,180 

3,201 

3,223 

3,245 

3,267 

3,289 

3,331 

30 

3,333 

3,356 

3,378 

3,400 

3,423 

3,445 

3,468 

3,491 

3,513 

3,536 

31 

3,559 

3,582 

3,605 

3,628 

3,652 

3,675 

3,698 

3,722 

3,745 

3,769 

32 

3,793 

3,816 

3,840 

3,864 

3,888 

3,912 

3,936 

3,960 

3,985 

4,009 

33 

4,033 

4,058 

4,082 

4,107 

4,132 

4,156 

4,181 

4,206 

4,231 

4,256 

34 

4,281 

4,307 

4,332 

4,357 

4,383 

4,408 

4,434 

4,460 

4,485 

4,511 

35 

4,537 

4,563 

4,589 

4,615 

4,641 

4,668 

4,694 

4,720 

4,747 

4,773 

36 

4,800 

4,827 

4,853 

4,880 

4,907 

4,934 

4,961 

4,988 

5,016 

5,043 

37 

5,070 

5,098 

5,125 

5,153 

5,181 

5,208 

5,236 

5,264 

5,292 

5,320 

38 

5,348 

5,376 

5,405 

5,433 

5,461 

5,490 

5,518 

5,547 

5,576 

5,604 

39 

5,633 

5,662 

5,691 

5,720 

5,749 

5,779 

5,808 

5,837 

5,867 

5,896 

40 

5,926 

5,956 

5,985 

6,015 

6,045 

6,075 

6,105 

6,135 

6,165 

6,196 

41 

6,226 

6,256 

6,287 

6,317 

6,348 

6,379 

6,409 

6,440 

6,471 

6,502 

42 

6,533 

6,564 

6,596 

6,627 

6,658 

6,690 

6,721 

6,763 

6,785 

6,816 

43 

6,848 

6,880 

6,912 

6,944 

6,976 

7,008 

7,041 

7,073 

7,105 

7,138 

44 

7,170 

7,203 

7,236 

7,268 

7,301 

7,334 

7,367 

7,400 

7,433 

7,467 

45 

7,500 

7,533 

7,567 

7,600 

7,634 

7,668 

7,701 

7,735 

7,769 

7,803 

46 

7,837 

7,871 

7,905 

7,940 

7,974 

8,008 

8,043 

8,077 

8,112 

8,147 

STRUCTURAL  DIAGRAMS   AND    TABLES 


209 


TABLE  31  (Concluded) 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  LEVEL  CUT 
Side  Slopes  1  to  1 


°3 


47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 


.0 

.1 

* 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

8,181 
8,533 

8,216 
8,569 

8,251 
8,605 

8,286 
8,640 

8,321 
8,676 

8,356 

8,712 

8,392 

8,748 

8,427 
8,784 

8,462 
8,820 

8,498 
8,856 

8,893 

8,929 

8,965 

9,002 

9,038 

9,075 

9,112 

9,148 

9,185 

9,222 

9,259 

9,296 

9,333 

9,371 

9,408 

9,445 

9,483 

9,520 

9,558 

9,596 

9,633 

9,671 

9,709 

9,747 

9,785 

9,823 

9,861 

9,900 

9,938 

9,976 

10,015 

10,053 

10,092 

10,131 

10,169 

10,208 

10,247 

10,286 

10,325 

10,364 

10,404 

10,443 

10,482 

10,522 

10,561 

10,601 

10,641 

10,680 

10,720 

10,760 

10,800 

10,840 

10,880 

10,920 

10,961 

11001 

11,041 

11,082 

11,122 

11,163 

11,204 

11,244 

11,285 

11,326 

11,367 

11,408 

11,449 

11,491 

11,532 

11,573 

11,615 

11,656 

11,698 

11,740 

11,781 

11,823 

11,865 

11,907 

11,949 

11,991 

12,033 

12,076 

12,118 

12,160 

12,203 

12,245 

12,288 

12,331 

12,373 

12,416 

12,459 

12,502 

12,545 

12,588 

12,632 

12,675 

12,718 

12,762 

12,805 

12,849 

12,893 

12,936 

12,980 

13,024 

13,068 

13,112 

13,156 

13,200 

13,245 

13,289 

13,333 

TABLE  32 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  LEVEL  CUT 
Side  Slopes  1 1  to  1 


Depth  of 
Center  Cut, 
in  Feet 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

0 

0.0 

0.0 

0.2 

0.5 

0.9 

1.4 

2.0 

2.7 

3.6 

4.5 

1 

5.6 

6.7 

8.0 

9.4 

10.9 

12.5 

14.2 

16.1 

18.0 

20.1 

2 

22 

24 

27 

29 

32 

35 

38 

41 

44 

47 

3 

50 

53 

57 

60 

64 

68 

72 

76 

80 

84 

4 

89 

93 

98 

103 

108 

112 

118 

123 

128 

133 

5 

139 

144 

150 

156 

162 

168 

174 

180 

187 

193 

6 

200 

207 

214 

222 

228 

235 

242 

249 

257 

264 

7 

272 

280 

288 

296 

304 

312 

321 

329 

338 

347 

8 

356 

364 

374 

383 

392 

401 

411 

420 

430 

440 

9 

450 

460 

470 

480 

491 

501 

512 

522 

533 

544 

10 

556 

567 

577 

589 

601 

612 

624 

636 

648 

660 

11 

672 

684 

697 

709 

722 

735 

748 

760 

774 

787 

12 

800 

813 

827 

840 

854 

868 

882 

896 

910 

924 

13 

939 

953 

968 

983 

998 

1,012 

1,028 

1,043 

1,058 

1,073 

14 

1,089 

1,104 

1,120 

1,136 

1,152 

1,168 

1,184 

1,200 

1,217 

1,233 

15 

1,250 

1,267 

1,284 

1,300 

1,318 

1,335 

1,352 

1,369 

1,387 

1,404 

210 


WORKING  DATA   FOR   IRRIGATION   ENGINEERS 


TABLE  32  (Concluded} 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  LEVEL  CUT 
Side  Slopes  1 1   to  1 


I  Depth  of 
1  Center  Cut, 
I  in  Feet 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

16 

1,422 

1,440 

1,458 

1,476 

1,494 

1,512 

1,531 

1,549 

1,568 

1,587 

17 

1,606 

1,624 

1,644 

1,663 

1,682 

1,701 

1,721 

1,740 

1,760 

1,780 

18 

1,800 

1,820 

1,840 

1,860 

1,881 

1,901 

1,922 

1,943 

1,964 

1,984 

19 

2,006 

2,027 

2,048 

2,069 

2,091 

2,112 

2,134 

2,156 

2,178 

2,200 

20 

2,222 

2,244 

2,267 

2,289 

2,311 

2,335 

2,358 

2,380 

2,404 

2,427 

21 

2,450 

2,473 

2,497 

2,520 

2,544 

2,568 

2,592 

2,616 

2,640 

2,664 

22 

2,689 

2,713 

2,738 

2,763 

2,788 

2,812 

2,838 

2,863 

2,888 

2,913 

23 

2,939 

2,964 

2,990 

3,016 

3,042 

3,068 

3,094 

3,120 

3,147 

3,173 

24 

3,200 

3,227 

3,254 

3,280 

3,308 

3,335 

3,362 

3,389 

3,417 

3,444 

25 

3,472 

3,500 

3,528 

3,556 

3,584 

3,612 

3,641 

3,669 

3,698 

3,727 

26 

3,756 

3,784 

3,814 

3,843 

3,872 

3,901 

3,931 

3,960 

3,990 

4,020 

27 

4,050 

4,080 

4,110 

4,140 

4,171 

4,201 

4,232 

4,263 

4,294 

4,324 

28 

4,356 

4,387 

4,418 

4,449 

4,481 

4,512 

4,544 

4,576 

4,608 

4,640 

29 

4,672 

4,704 

4,737 

4,769 

4,802 

4,835 

4,868 

4,900 

4,934 

4,967 

30 

5,000 

5,033 

5,067 

5,100 

5,134 

5,168 

5,202 

5,236 

5,270 

5,304 

31 

5,339 

5,373 

5,408 

5,443 

5,478 

5,512 

5,548 

5,583 

5,618 

5,653 

32 

5,689 

5,724 

5,760 

5,796 

5,832 

5,868 

5,904 

5,940 

5,977 

6,013 

33 

6,050 

6,087 

6,124 

6160 

6,198 

6,235 

6,272 

6,309 

6,347 

6,384 

34 

6,422 

6,460 

6,498 

6,536 

6,574 

6,612 

6,651 

6,689 

6,728 

6,767 

35 

6,806 

6,844 

6,884 

6,923 

6,962 

7,001 

7,041 

7,080 

7,120 

7,160 

36 

7,200 

7,240 

7,280 

7,320 

7,361 

7,401 

7,442 

7,483 

7,524 

7,564 

37 

7,606 

7,647 

7,688 

7,729 

7,771 

7,812 

7,854 

7,896 

7,938 

7,980 

38 

8,022 

8,064 

8,107 

8,149 

8,192 

8,235 

8,278 

8,320 

8,364 

8,407 

39 

8,450 

8,493 

8,537 

8,580 

8,624 

8,668 

8,712 

8,756 

8,800 

8,844 

40 

8,889 

8,933 

8,978 

9,023 

9,068 

9,112 

9,158 

9,203 

9,248 

9,293 

41 

9,339 

9,384 

9,430 

9,476 

9,522 

9,568 

9,614 

9,660 

9,707 

9,753 

42 

9,800 

9,847 

9,894 

9,940 

9,988 

10,035 

10,082 

10,129 

10,177 

10,224 

43 

10,272 

10,320 

10,368 

10,416 

10,464 

10,512 

10,561 

10,609 

10,658 

10,707 

44 

10,756 

10,804 

10,854 

10,903 

10,952 

11,001 

11,051 

11,100 

11,150 

11,200 

45 

11,250 

11,300 

11,350 

11,400 

11,451 

11,501 

11,552 

11,603 

11,654 

11,704 

46 

11,756 

11,807 

11,858 

11,909 

11,961 

12,012 

12,064 

12,116 

12,168 

12,220 

47 

12,272 

12,324 

12,377 

12,429 

12,482 

12,535 

12,588 

12,640 

12,694 

12,747 

48 

12,800 

12,853 

12,907 

12,960 

13,014 

13,068 

13,122 

13,176 

13,230 

13,284 

49 

13,339 

13,393 

13,448 

13,503 

13,558 

13,612 

13,668 

13,723 

13,778 

13,833 

50 

13,889 

13,944 

14,000 

14,056 

14,112 

14,168 

14,224 

14,280 

14,337 

14,392 

51 

14,450 

14,507 

14,564 

14,620 

14,678 

14,735 

14,792 

14,849 

14,987 

14,964 

52 

15,022 

15,080 

15,138 

15,196 

15,254 

15,312 

15,371 

15,430 

15,489 

15,548 

53 

15,606 

15,664 

15,724 

15,783 

15,842 

15,901 

15,961 

16,020 

16,080 

16,140 

54 

16,200 

16,260 

16,320 

16,380 

16,441 

16,501 

16,562 

16,623 

16,684 

16,744 

55 

16,806 

16,867 

16,928 

16,989 

17,051 

17,112 

17,174 

17,236 

17,298 

17,360 

56 

17,422 

17,484 

17,547 

17,609 

17,672 

17,735 

17,798 

17,860 

17,924 

17,987 

57 

18,050 

18,113 

18,177 

18,240 

18,304 

18,368 

18,432 

18,496 

18,560 

18,624 

58 

18,689 

18,753 

18,818 

18,883 

18,948 

19,012 

19,078 

19,143 

19,208 

19,273 

59 

19,339 

19,404 

19,470 

19,536 

19,602 

19,668 

19,734 

19,800 

19,867 

19,933 

60 

20  000 

STRUCTURAL  DIAGRAMS   AND   TABLES 


211 


TABLE  33 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  LEVEL  CUT 
Side  Slopes  2  to  1 


Depth  of  1 
Center  Cut, 
in  Feet 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

0 

0.0 

0.1 

0.3 

0.7 

1.2 

1.9 

2.7 

3.6 

4.7 

6.0 

1 

7.4 

9.0 

10.7 

12.5 

14.5 

16.7 

19.0 

21.4 

24.0 

26.7 

2 

30 

33 

36 

39 

43 

46 

50 

54 

58 

62 

3 

67 

71 

76 

81 

86 

91 

96 

101 

107 

113 

4 

119 

125 

131 

137 

143 

150 

157 

164 

171 

178 

5 

185 

193 

200 

208 

216 

224 

232 

241 

249 

258 

6 

267 

276 

285 

294 

303 

313 

323 

333 

343 

353 

7 

363 

373 

384 

395 

406 

417 

428 

439 

451 

462 

8 

474 

486 

498 

510 

523 

535 

548 

561 

574 

587 

9 

600 

613 

627 

641 

655 

669 

683 

697 

711 

726 

10 

741 

756 

771 

786 

801 

817 

832 

848 

864 

880 

11 

896 

913 

929 

946 

963 

980 

997 

1,014 

1,031 

1,049 

12 

1,067 

1,084 

1,103 

1,121 

1,139 

1,157 

1,176 

1,195 

1,214 

1,233 

13 

1,252 

1,271 

1,291 

1,310 

1,330 

1,350 

1,370 

1,390 

1,411 

1,431 

14 

1,452 

1,473 

1,494 

1,515 

1,536 

1,557 

1,579 

1,601 

1,623 

1,645 

15 

1,667 

1,689 

1,711 

1,734 

1,757 

1,780 

1,803 

1,826 

1,849 

1,873 

16 

1,896 

1,920 

1,944 

1,968 

1,992 

2,017 

2,041 

2,066 

2,091 

2,116 

17 

2,141 

2,166 

2,191 

2,217 

2,243 

2,269 

2,295 

2,321 

2,347 

2,373 

18 

2,400 

2,427 

2,454 

2,481 

2,508 

2,535 

2,563 

2,590 

2,618 

2,646 

19 

2,674 

2,702 

2,731 

2,759 

2,788 

2,817 

2,846 

2,875 

2,904 

2,938 

20 

2,963 

2,993 

3,023 

3,053 

3,083 

3,113 

3,143 

3,174 

3,205 

3,236 

21 

3,267 

3,298 

3,329 

3,361 

3,392 

3,424 

3,456 

3,488 

o,520 

3,553 

22 

3,585 

3,618 

3,651 

3,684 

3,717 

3,750 

3,783 

3,817 

3,851 

3,885 

23 

3,919 

3,953 

3,987 

4,021 

4,056 

4,091 

4,126 

4,161 

4,196 

4,231 

24 

4,267 

4,302 

4,338 

4,374 

4,410 

4,446 

4,483 

4,519 

4,556 

4,593 

25 

4,630 

4,667 

4,704 

4,741 

4,779 

4,817 

4,855 

4,893 

4,931 

4,969 

26 

5,007 

5,046 

5,085 

5,124 

5,163 

5,202 

5,241 

5,281 

5,320 

5,360 

27 

5,400 

5,440 

5,480 

5,521 

5,561 

5,602 

5,643 

5,684 

5,725 

5,766 

28 

5,807 

5,849 

5,891 

5,933 

5,975 

6,017 

6,059 

6,101 

6,144 

6,187 

29 

6,230 

6,273 

6,316 

6,359 

6,403 

6,446 

6,490 

6,534 

6,578 

6,622 

30 

6,667 

6,711 

6,756 

6,801 

6,846 

6,891 

6,936 

6,981 

7,027 

7,073 

31 

7,119 

7,165 

7,211 

7,257 

7,303 

7,350 

7,397 

7,444 

7,491 

7,538 

32 

7,585 

7,633 

7,680 

7,728 

7,776 

7,824 

7,872 

7,921 

7,969 

8,018 

33 

8,067 

8,116 

8,165 

8,214 

8,263 

8,313 

8,363 

8,413 

8,463 

8,513 

34 

8,563 

8,613 

8,664 

8,715 

8,766 

8,817 

8,868 

8,919 

8,971 

9,022 

35 

9,074 

9,126 

9,178 

9,230 

9,283 

9,335 

9,388 

9,441 

9,494 

9,547 

36 

9,600 

9,653 

9,707 

9,761 

9,815 

9,869 

9,923 

9,977 

10,031 

10,086 

37 

0,141 

10,196 

10,251 

10,306 

10,361 

10,417 

10,472 

10,528 

10,584 

10,640 

38 

0,696 

10,753 

10,809 

10,866 

10,923 

10,980 

11,037 

11,094 

11,151 

11,209 

39 

11,267 

11,325 

11,383 

11,441 

11,499 

11,557 

11,616 

11,675 

11,734 

11,793 

40 

11,852 

11,911 

11,971 

12,030 

12,090 

12,150 

12,210 

12,270 

12,331 

12,391 

41 

2,452 

12,513 

12,574 

12,635 

12,696 

12,757 

12,819 

12,881 

12,^43 

13,005 

42 

13,067 

13,129 

13,191 

13,254 

13,317 

13,380 

13,443 

13,506 

13,569 

13,633 

43 

13,696 

13,760 

13,824 

13,888 

13,952 

14,017 

14,081 

14,146 

14,211 

4,276 

44 

14,341 

14,406 

14,471 

14,537 

14,603 

14,669 

14,735 

14,801 

14,867 

4,933 

212 


WORKING  DATA   FOR  IRRIGATION   ENGINEERS 


TABLE  33  (Concluded) 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  LEVEL  CUT 
Side  Slopes  2  to  1 


1  Depth  of  !| 
Center  Cut,; 
|  in  Feet 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

45 

15,000 

15,067 

15,134 

15,201 

15,268 

15,335 

15,403 

15,470 

15,538 

15,606 

46 

15,674 

15,742 

15,811 

15,879 

15,948 

16,017 

16,086 

16,155 

16,224 

16,293 

47 

16,363 

16,433 

16,503 

16,573 

16,643 

16,713 

16,783 

16,854 

16,925 

16,996 

48 

17,067 

17,138 

17,209 

17,281 

17,352 

17,424 

17,496 

17,568 

17,640 

17,713 

49 

17,785 

17,858 

17,931 

18,004 

18,077 

18,150 

18,223 

18,297 

18,371 

18,445 

50 

18,519 

18,593 

18,667 

18,741 

18,816 

18,891 

18,966 

19,041 

19,116 

19,191 

51 

19,267 

19,342 

19,418 

19,494 

19,570 

19,646 

19,723 

19,799 

19,876 

19,953 

52 

20,030 

20,107 

20,184 

20,261 

20,339 

20,417 

20,495 

20,573 

20,651 

20,729 

53 

20,807 

20,886 

20,965 

21,044 

21,123 

21,202'21,281 

21,361 

21,440 

21,520 

54 

21,600 

21,680 

21,760 

21,841 

21,921 

22,002:22,08322,164 

22,245 

22,326 

55 

22,407 

22,489 

22,571 

22,653 

22,735 

22,81722,89922,981 

23,064 

23,147 

56 

23,230 

23,313 

23,396 

23,479 

23,563 

23,64623,73023,814 

23,898 

23,982 

57 

24,067 

24,151 

24,236 

24,321 

24,406 

24,49124,57624,661 

24,747 

24,833 

58 

24,919 

25,005 

25,091 

25,177 

25,263 

25,35025,44725,524 

25,611 

25,698 

59 

25,785 

25,873 

25,960 

26,048 

26,136 

26,22426,31226,401 

26,489 

26,578 

60 

26,667 

TABLE  34 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  LEVEL  CUT 
Side  Slopes  3  to  1 


Depth  of  II 
Center  Cut, 
in  Feet 

.0 

.1 

o 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

0 

0.0 

0.1 

0.4 

1.0 

1.8 

2.8 

4.0 

5.4 

7.1 

9.0 

1 

11  1 

13.4 

16.0 

18.8 

21.8 

25.0 

28.4 

32.2 

36.1 

40.1 

2 

44 

49 

54 

59 

64 

69 

75 

81 

87 

93 

3 

100 

106 

114 

121 

128 

136 

144 

152 

160 

168 

4 

178 

187 

196 

205 

215 

225 

235 

245 

256 

267 

5 

278 

289 

300 

312 

324 

336 

348 

361 

373 

387 

6 

400 

413 

427 

441 

445 

469 

484 

499 

514 

529 

7 

544 

560 

576 

592 

608 

625 

642 

659 

676 

693 

8 

711 

729 

747 

765 

784 

803 

822 

841 

860 

880 

9 

900 

920 

940 

961 

982 

1,003 

1,024 

1,045 

1,067 

1,089 

10 

1,111 

1,133 

1,156 

1,179 

1,202 

1,225 

1,248 

1,272 

1,296 

1,320 

11 

1,344 

1,369 

1,394 

1,419 

1,444 

1,469 

1,495 

1,521 

1,547 

1,573 

12 

1,600 

1,627 

1,654 

1,681 

1,708 

1,736 

1,764 

1,792 

1,820 

1,849 

13 

1,878 

1,907 

1,936 

1,965 

1,995 

2,025 

2,055 

2,085 

2,116 

2,147 

14 

2,178 

2,209 

2,240 

2,272 

2,304 

2,336 

2,368 

2,401 

2,434 

2,467 

STRUCTURAL  DIAGRAMS   AND   TABLES 


213 


TABLE  34  (Concluded} 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  LEVEL  CUT 
Side  Slopes  3  to  1 


Depth  of 
Center  Cut, 
in  Feet 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

15 

2,500 

2,533 

2,567 

2,601 

2,635 

2,669 

2,704 

2,739 

2,774 

2,809 

16 

2,844 

2,880 

2,916 

2,952 

2,988 

3,025 

3,062 

3,099 

3,136 

3,173 

17 

3,211 

3,249 

3,287 

3,325 

3,364 

3,403 

3,442 

3,481 

3,520 

3,560 

18 

3,600 

3,640 

3,680 

3,721 

3,762 

3,803 

3,844 

3,885 

3,927 

3,969 

19 

4,011 

4,053 

4,096 

4,139 

4,182 

4,225 

4,268 

4,312 

4,356 

4,400 

20 

4,444 

4,489 

4,534 

4,579 

4,624 

4,669 

4,715 

4,761 

4,807 

4,853 

21 

4,900 

4,947 

4,994 

5,041 

5,088 

5,137 

5,184 

5,232 

5,280 

5,329 

22 

5,378 

5,427 

5,476 

5,525 

5,575 

5,625 

5,675 

5,725 

5,776 

5,827 

23 

5,878 

5,929 

5,980 

6,032 

6,084 

6,136 

6,188 

6,240 

6,294 

6,346 

24 

6,400 

6,453 

6,507 

6,561 

6,615 

6,669 

6,724 

6,779 

6,834 

6,889 

25 

6,944 

7,000 

7,056 

7,112 

7,168 

7,225 

7,282 

7,339 

7,396 

7,453 

26 

7,511 

7,569 

7,627 

7,685 

7,744 

7,803 

7,862 

7,921 

7,980 

8,040 

27 

8,100 

8,160 

8,220 

8,281 

8,342 

8,403 

8,464 

8,525 

8,587 

8,649 

28 

8,711 

8,773 

8,836 

8,899 

8,962 

9,025 

9,088 

9,152 

9,216 

9,280 

29 

9,344 

9,409 

9,474 

9,539 

9,604 

9,669 

9,735 

9,801 

9,867 

9,993 

30 

10,000 

10,067 

10,134 

10,201 

10,268 

10,336 

10,404 

10,472 

10,540 

10,609 

31 

10,678 

10,747 

10,816 

10,885 

10,955 

11,025 

11,095 

11,165 

11,236 

11,307 

32 

11,378 

11,449 

11,520 

11,592 

11,664 

11,736 

11,808 

11,881 

11,954 

12,027 

33 

12,100 

12,173 

12,247 

12,321 

12,395 

12,469 

12,544 

12,619 

12,694 

12,769 

34 

12,844 

12,920 

12,996 

13,072 

13,148 

13,225 

13,302 

13,379 

13,456 

13,533 

35 

13,611 

13,689 

13,767 

13,845 

13,924 

14,003 

14,082 

14,161 

14,240 

14,320 

36 

14,400 

14,480 

14,560 

14,641 

14,722 

14,803 

14,884 

14,965 

15,047 

15,129 

37 

15,211 

15,293 

15,376 

15,459 

15,542 

15,625 

15,708 

15,792 

15,876 

15,960 

38 

16,044 

16,129 

16,214 

16,299 

16,384 

16,469 

16,555 

16,641 

16,727 

16,813 

39 

16,900 

16,987 

17,074 

17,161 

17,248 

17,336 

17,424 

17,512 

17,600 

17,689 

40 

17,778 

17,867 

17,956 

18,045 

18,135 

18,225 

18,315 

18,405 

18,496 

18,587 

41 

18,678 

18,769 

18,860 

18,952 

19,044 

19,136 

19,228 

19,321 

19,414 

19,507 

42 

19,600 

19,693 

19,787 

19,881 

19,975 

20,069 

20,164 

20,259 

20,354 

20,449 

43 

20,544 

20,640 

20,736 

20,832 

20,928 

21,025 

21,122 

21,219 

21,316 

21,413 

44 

21,511 

21,609 

21,707 

21,805 

21,904 

22,003 

22,102 

22,201 

22,300 

22,400 

45 

22,500 

22,600 

22,700 

22,801 

22,902 

23,003 

23,104 

23,205 

23,307 

23,409 

46 

23,511 

23,613 

23,716 

23,819 

23,922 

24,025 

24,128 

24,232 

24,336 

24,440 

47 

24,544 

24,649 

24,754 

24,859 

24,964 

25,069 

25,175 

25,281 

25,387 

25,493 

48 

25,600 

25,707 

25,814 

25,921 

26,029 

26,136 

26,244 

26,352 

26,460 

26,569 

49 

26,678 

26,787 

26,896 

27,005 

27,115 

27,225 

27,335 

27,445 

27,556 

27,667 

50 

27,778 

27,889 

28,000 

28,112 

28,224 

28,336 

28,448 

28,561 

28,674 

28,787 

51 

28,900 

29,013 

29,127 

29,241 

29,355 

29,469 

29,584 

29,699 

29,814 

29,929 

52 

30,044 

30,160 

30,276 

30,392 

30,508 

30,625 

30,742 

30,859 

30,976 

31,093 

53 

31,211 

31,329 

31,447 

31,565 

31,684 

31,80331,922 

32,041 

32,160 

32,280 

54 

32,400 

32,520 

32,640 

32,761 

32,882 

33,003 

33,124 

33,245 

33,367 

33,489 

55 

33,611 

33,733 

33,856 

33,979 

34,102 

34,225 

34,348 

34,472 

34,596 

34,720 

56 

34,844 

34,969 

35,094 

35,219 

35,344 

35,459 

35,595 

35,721 

35,847 

35,973 

57 

36,100 

36,227 

35,354 

36,481 

36,608 

36,736 

36,864 

36,992 

37,120 

37,249 

58 

37,378 

37,507 

37,636 

37,765 

37,895 

38,025 

38,155 

38,285 

38,416 

38,547 

59 

38,678 

38,809 

38,940 

39,072 

39,204 

39,336 

39,468 

39,601 

39,734 

39,867 

,  60 

40,000 

214 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


TABLE  35 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  CUT  ON 

SLOPING  GROUND 

Side  Slopes  1  to  1 


<O3 
£* 

5S| 
ISa 

SURFACE  SLOPE  OF  GROUND  IN  PER  CENT 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

1r\ 

.u 
1.5 

8 

8 

9 

9 

9 

9 

10 

10 

11 

12 

13 

2.0 

15 

15 

16 

16 

16 

17 

18 

19 

20 

21 

23 

2.5 

23 

24 

24 

25 

25 

27 

27 

29 

31 

33 

36 

3.0 

33 

33 

34 

35 

36 

38 

39 

42 

44 

47 

52 

3.5 

46 

46 

47 

48 

49 

51 

54 

57 

60 

65 

70 

4.0 

59 

60 

61 

63 

65 

67 

70 

74 

79 

85 

92 

4.5 

76 

77 

78 

80 

83 

85 

89 

94 

100 

107 

117 

5.0 

94 

95 

97 

99 

102 

106 

111 

117 

124 

133 

145 

5.5 

113 

114 

117 

120 

123 

128 

133 

141 

149 

161 

175 

6.0 

134 

136 

139 

142 

146 

152 

158 

167 

177 

191 

208 

6.5 

157 

160 

163 

166 

172 

178 

186 

196 

208 

224 

244 

7.0 

183 

185 

189 

193 

199 

206 

215 

227 

242 

260 

283 

7.5 

210 

212 

217 

222 

229 

237 

248 

261 

278 

299 

325 

8.0 

239 

242 

247 

253 

261 

270 

282 

297 

316 

340 

370 

8.5 

270 

274 

279 

286 

295 

305 

319 

336 

357 

384 

418 

9.0 

303 

307 

312 

320 

330 

342 

357 

376 

400 

430 

468 

9.5 

338 

342 

348 

356 

367 

381 

398 

419 

446 

479 

522 

10.0 

374 

378 

385 

395 

406 

422 

441 

464 

494 

531 

578 

10.5 

412 

417 

425 

436 

448 

465 

486 

512 

545 

585 

637 

11.0 

453 

458 

467 

478 

492 

510 

533 

562 

598 

642 

700 

11.5 

495 

501 

510 

523 

538 

558 

583 

615 

653 

702 

765 

12.0 

539 

545 

555 

569 

586 

607 

634 

669 

711 

764 

833 

12.5 

585 

592 

603 

618 

637 

659 

689 

726 

772 

830 

904 

13.0 

632 

640 

652 

668 

689 

713 

745 

785 

835 

897 

978 

13.5 

681 

691 

703 

720 

743 

769 

803 

847 

900 

967 

,054 

14.0 

733 

743 

756 

774 

799 

827 

864 

911 

968 

1,040 

,134 

14.5 

787 

797 

811 

831 

857 

887 

927 

977 

1,039 

1,116 

,216 

15.0 

841 

852 

868 

888 

916 

949 

994 

,045 

1,111 

1,194 

,301 

15.5 

898 

910 

927 

949 

978 

1,014 

1,059 

,116 

,187 

1,276 

,390 

16.0 

957 

970 

987 

1,011 

1,042 

1,080 

1,128 

,189 

,264 

1,359 

,480 

16.5 

1,018 

1,031 

1,050 

1,075 

1,1-08 

1,148 

1,199 

,265 

,344 

1,445 

,573 

17.0 

1,080 

1,095 

1,115 

1,141 

1,176 

,219 

1,273 

,343 

,427 

1,534 

,669 

17.5 

1,145 

1,160 

1,182 

1,209 

1,246 

,292 

1,349 

,423 

,512 

1,626 

,770 

18.0 

1,212 

1,227 

1,250 

1,280 

1,319 

,368 

1,428 

,506 

,600 

1,720 

,874 

18.5 

1,281 

1,297 

1,321 

1,353 

1,394 

,445 

1,509 

,591 

,691 

1,817 

,980 

19.0 

1,351 

1,368 

1,393 

1,426 

1,470 

,523 

1,591 

1,678 

,783 

1,916 

2,088 

19.5 

1,422 

1,440 

1,467 

1,502 

1,548 

,604 

1,676 

1,767 

1,878 

2,018 

2,199 

20.0 

1,496 

1,515 

1,542 

1,580 

1,628 

,687 

1,763 

1,859 

1,975 

2,123 

2,313 

20.5 

1,572 

1,592 

1,620 

1,660 

1,710 

1,773 

1,852 

1,953 

2,075 

2,230 

2,430 

21.0 

1,649 

1,670 

1,701 

1,742 

1,795 

1,861 

1,943 

2,049 

2,178 

2,340 

2,550 

21.5 

1,729 

1,751 

1,783 

1,826 

1,882 

1,951 

2,037 

2,148 

2,283 

2,453 

2,673 

22.0 

1,811 

1,834 

1,868 

1,913 

1,971 

2,043 

2,134 

2,250 

2,391 

2,569 

2,800 

22.5 

1,894 

1,918 

1,953 

2,001 

2,061 

2,136 

2,231 

2,353 

2,501 

2,687 

2,928 

23.0 

1,979 

2,004 

2,041 

2,090 

2,153 

2,232 

2,331 

2,458 

2,613 

2,808 

3,059 

STRUCTURAL   DIAGRAMS   AND   TABLES 


215 


TABLE   35  (Concluded) 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  CUT  ON 

SLOPING  GROUND 

Side  Slopes  1  to  1 


Depth  of  |i 
Center  Cut,  i 
in  Feet 

SURFACE  SLOPE  OF  GROUND  IN  PER  CENT 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

23.5 

2,065 

2,091 

2,130 

2,181 

2,247 

2,330 

2,434 

2,566 

2,728 

2,931 

3,194 

24.0 

2,154 

2,181 

2,221 

2,275 

2,344 

2,430 

2,539 

2,677 

2,845 

3,057 

3,331 

24.5 

2,245 

2,274 

2,315 

2,371 

2,443 

2,533 

2,646 

2,790 

2,965 

3,186 

3,472 

25.0 

2,338 

2,368 

2,411 

2,469 

2,545 

2,637 

2,755 

2,905 

3,088 

3,318 

3,615 

25.5 

2,432 

2,463 

2,508 

2,568 

2,647 

2,743 

2,866 

3,022 

3,212 

3,451 

3,761 

26.0 

2,529 

2,561 

2,608 

2,670 

2,752 

2,852 

2,980 

3,142 

3,340 

3,588 

3,910 

26.5 

2,627 

2,661 

2,709 

2,774 

2,859 

2,963 

3,095 

3,264 

3,469 

3,727 

4,062 

27.0 

2,727 

2,762 

2,813 

2,880 

2,968 

3,076 

3,212 

3,388 

3,601 

3,869 

4,217 

27.5 

2,829 

2,865 

2,918 

2,988 

3,079 

3,191 

3,332 

3,515 

3,736 

4,014 

4,374 

28.0 

2,932 

2,970 

3,024 

3,097 

3,191 

3,308 

3,454 

3,643 

3,872 

4,161 

4,534 

.28.5 

3,038 

3,077 

3,133 

3,208 

3,306 

3,427 

3,579 

3,775 

4,012 

4,311 

4,698 

29.0 

3,146 

3,187 

3,245 

3,322 

3,423 

3,548 

3,706 

3,909 

4,154 

4,464 

4,864 

29.5 

3,255 

3,297 

3,357 

3,438 

3,542 

3,671 

3,835 

4,045 

4,298 

4,619 

5,033 

30.0 

3,367 

3,409 

3,471 

3,555 

3,663 

3,797 

3,967 

4.183 

4,445 

4,777 

5,205 

30.5 

3,480 

3,524 

3,588 

3,675 

3,786 

3,924 

4,100 

4,323 

4,595 

4,937 

5,380 

31.0 

3,595 

3,641 

3,707 

3,798 

3,911 

4,054 

4,236 

4,466 

4,747 

5,100 

5,558 

31.5 

3,712 

3,759 

3,828 

3,920 

4,039 

4,187 

4,374 

4,612 

4,901 

5,266 

5,739 

32.0 

3,831 

3,880 

3,951 

4,046 

4,169 

4,322 

4,514 

4,760 

5,058 

5,435 

5,923 

32.5 

3,952 

4,002 

4,075 

4,173 

4,300 

4,457 

4,656 

4,909 

5,217 

5,606 

6,109 

33.0 

4,074 

4,126 

4,201 

4,302 

4,433 

4,595 

4,800 

5,061 

5,379 

5,780 

6,298 

33.5 

4,198 

4,252 

4,329 

4,433 

4,568 

4,735 

4,946 

5,215 

5,543 

5,956 

6,491 

34.0 

4,324 

4,379 

4,459 

4,566 

4,705 

4,877 

5,095 

5,372 

5,710 

6,135 

6,686 

34.5 

4,452 

4,509 

4,592 

4,702 

4,845 

5,022 

5,246 

5,531 

5,879 

6,317 

6,884 

35.0 

4,583 

4,641 

4,726 

4,839 

4,987 

5,169 

5,399 

5,693 

6,051 

6,502 

7,085 

35.5 

4,714 

4,774 

4,861 

4,978 

5,130 

5,317 

5,555 

5,856 

6,225 

6,689 

7,288 

36.0 

4,848 

4,910 

5,000 

5,120 

5,276 

5,469 

5,712 

6,023 

6,402 

6,879 

7,496 

36.5 

4,984 

5,048 

5,140 

5,263 

5,423 

5,621 

5,872 

6,191 

6,581 

7,071 

7,705 

37.0 

5,122 

5,187 

5,282 

5,408 

5,573 

5,776 

6,034 

6,362 

6,762 

7,266    7,918 

37.5 

5,261 

5,328 

5,426 

5,555 

5,725 

5,933 

6,198 

6,535 

6,946 

7,464    8,132 

38.0 

5,402 

5,471 

5,571 

5,705 

5,879 

6,093 

6,365 

6,711 

7,133 

7,665 

8,353 

38.5 

5,545 

5,615 

5,718 

5,855 

6,033 

6,254 

6,532 

6,888 

7,321 

7,867 

8,572 

39.0 

5,690 

5,763 

5,868 

6,008 

6,191 

6,418 

6,703 

7,069 

7,513 

8,073 

8,797 

39.5 

5,837 

5,912 

6,020 

6,164 

6,351 

6,584 

6,877 

7,252 

7,707 

8,282 

9,024 

40.0 

5,986 

6,062 

6,173 

6,321 

6,513 

6,752 

7,052 

7,436 

7,903 

8,493 

9,254 

40.5 

6,137 

6,215 

6,328 

6,480 

6,677 

6,921 

7,230 

7,623 

8,102 

8,706 

9,487 

41.0 

6,289 

6,369 

6,485 

6,641 

6,843 

7,093 

7,410 

7,813 

8,304 

8,922 

9,722 

41.5 

6,442 

6,524 

6,644 

6,803 

7,011 

7,266 

7,591 

8,004 

8,507 

9,140    9,961 

42.0 

6,599 

6,683 

6,806 

6,969 

7,181 

7,443 

7,775 

8,198 

8,713 

9,362  10,203 

42.5 

6,758 

6,844 

6,969 

7,136 

7,353 

7,622 

7,962 

8,395 

8,922 

9,587  10,447 

43.0 

6,917 

7,006 

7,134 

7,305 

7,527 

7,802 

8,150 

8,593  9,133 

9,814110,694 

43.5 

7,079 

7,170 

7,300 

7,476 

7,703 

7,984 

8,341 

8,794  9,347 

10,043  10,944 

44.0 

7,243 

7,335 

7,469 

7,648 

7,880 

8,169 

8,533 

8,997  9,563 

10,175  11,197 

216 


WORKING  DATA  FOR   IRRIGATION  ENGINEERS 


TABLE  36 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  CUT  ON 

SLOPING  GROUND 

Side  Slopes  1 1   to  1 


o3 

£$£ 

^ 

SURFACE  SLOPE  OF  GROUND  IN  PER  CENT 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

0.5 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

6 

1.0 

6 

6 

7 

7 

7 

8 

9 

11 

13 

18 

29 

1.5 

12 

13 

13 

14 

15 

17 

19 

22 

28 

39 

65 

2.0 

23 

23 

24 

26 

28 

38 

34 

41 

51 

70 

117 

2.5 

36 

37 

38 

41 

44 

48 

55 

64 

80 

109 

183 

3.0 

51 

53 

55 

58 

63 

69 

78 

92 

114 

157 

263 

3.5 

70 

72 

75 

79 

85 

94 

106 

125 

155 

213 

357 

4.0 

91 

94 

98 

104 

112 

123 

139 

163 

203 

278 

467 

4.5 

113 

118 

124 

132 

141 

155 

176 

206 

257 

352 

590 

5.0 

142 

146 

153 

162 

174 

192 

217 

255 

318 

435 

730 

5.5 

172 

177 

185 

195 

211 

232 

262 

309 

384 

526 

882 

6.0 

205 

211 

220 

233 

251 

276 

312 

368 

457 

624 

1,051 

6.5 

240 

248 

258 

273 

295 

324 

367 

431 

537 

735 

1,233 

7.0 

278 

287 

299 

317 

341 

375 

425 

500 

622 

852 

1,430 

7.5 

319 

329 

343 

363 

391 

430 

488 

574 

714 

978 

1,641 

8.0 

364 

375 

391 

414 

446 

491 

556 

654 

813 

,113 

1,870 

8.5 

411 

423 

441 

467 

503 

555 

627 

738 

918 

,257 

2,107 

9.0 

460 

474 

495 

524 

564 

622 

703 

827 

1,029 

,409 

2,364 

9.5 

513 

528 

552 

583 

628 

691 

783 

922 

,146 

,569 

2,633 

10.0 

569 

585 

611 

647 

697 

765 

868 

1,021 

,271 

,740 

2,919 

10.5 

627 

645 

673 

712 

768 

844 

956 

1,125 

,401 

,918 

3,217 

11.0 

687 

708 

739 

781 

843 

927 

1,049 

1,235 

,537 

2,104 

3,531 

11.5 

752 

774 

808 

855 

922 

1,013 

1,149 

1,350 

,680 

2,301 

3,860 

12.0 

819 

843 

879 

931 

,003 

1,103 

1,250 

1,470 

1,829 

2,504 

4,203 

12.5 

888 

914 

954 

1,010 

,089 

1,197 

1,356 

1,595 

1,985 

2,717 

4,560 

13.0 

961 

989 

03?, 

1,093 

,178 

1,295 

1  467 

1,725 

2,147 

2,939 

4,933 

13.5 

1,036 

1,066 

,112 

1,178 

,269 

1,396 

1,581 

1,860 

2,316 

3,170 

5,318 

14.0 

1,114 

1,147 

,196 

1,267 

,365 

1,502 

1,701 

2,001 

2,489 

3,410 

5,721 

14.5 

1,195 

1,230 

,284 

1,359 

,465 

1,612 

1,825 

2,146 

2,669 

3,657 

6,136 

15.0 

1,279 

1,316 

,374 

1,454 

,568 

1,724 

1,952 

2,297 

2,857 

3,914 

6,567 

15.5 

1,366 

1,406 

,467 

1,553 

,674 

1,841 

2,085 

2,453 

3,051 

4,179 

7,012 

16.0 

1,455 

1,498 

,563 

1,654 

,784 

1,961 

2,221 

3,613 

3,250 

4,453 

7,472 

16.5 

1,547 

1,593 

,662 

1,759 

,897 

2,085 

2,362 

2,779 

3,456 

4,735 

7,945 

17.0 

1,643 

1,691 

,765 

1,868 

2,014 

2,214 

2,507 

2,951 

3,670 

5,027 

8,435 

17.5 

1,741 

1,792 

,870 

1,979 

2,134 

2,346 

2,656 

3,126 

3,889 

5,326 

8,937 

18.0 

1,841 

1,896 

,979 

2,094 

2,258 

2,482 

2,809 

3,308 

4,114 

5,636 

9,456 

18.5 

1,945 

2,002 

2,090 

2,212 

2,385 

2,622 

2,967 

3,494 

4,346 

5,953 

9,988 

19.0 

2,051 

2,111 

2,205 

2,334 

2,516 

2,766 

3,130 

3,686 

4,585 

6,279 

10,535 

19.5 

2,160 

2,225 

2,322 

2,458 

2,650 

2,913 

3,299 

3,881 

4,828 

6,614 

11,097 

20.0 

2,272 

2,341 

2,442 

2,586 

2,787 

3,064 

3,472 

4,083 

5,079 

6,957 

11,673 

20.5 

2,387 

2,460 

2,566 

2,717 

2,929 

3,220 

3,648 

4,289 

5,337 

7,310 

12,265 

21.0 

2,506 

2,581 

2,692 

2,851 

3,073 

3,379 

3,828 

4,502 

5,600 

7,670 

12,871 

21.5 

2,627 

2,705 

2,822 

2,988 

3,221 

3,541 

4,013 

4,719 

5,870 

8,040 

13,491 

22.0 

2,751 

2,832 

2,955 

3,129 

3,373 

3,708 

4,201 

4,941 

6,147 

8,417 

14,127 

22.5 

2,877 

2,962 

3,090 

3,272 

3,527 

3,878 

4,394 

5,168 

6,429 

8,804  14,775 

STRUCTURAL  DIAGRAMS   AND   TABLES 


217 


AMOUNT   OF   MATERIAL   IN 


TABLE  36  (Concluded} 

CUBIC   YARDS   PER   100 
SLOPING  GROUND 

Side  Slopes  l.\  to  1 


LINEAR  FEET  OF  CUT  ON 


>«  3 
0<J 

•sSl 

a  fife 

QS.S 

SURFACE  SLOPE  OF  GROUND  IN  PER  CENT 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

23.0 

3,007 

3,096 

3,229 

3,420 

3,686 

4,053 

4,592 

5,400 

6,718 

9,201 

15,440 

23.5 

3,139 

3,232 

3,372 

3,570 

3,848 

4,231 

4,794 

5,638 

7,013 

9,606 

16,118 

24.0 

3,274 

3,371 

3,517 

3,724 

4,014 

4,413 

5,000 

5,881 

7,314 

10,019 

16,812 

24.5 

3,412 

3,513 

3,665 

3,881 

4,183 

4,599 

5,211 

6,129 

7,622 

10,441 

17,519 

25.0 

3,552 

3,657 

3,816 

4,040 

4,355 

4,788 

5,425 

6,382 

7,936 

10,871 

18242 

25.5 

3,695 

3,804 

3,970 

4,203 

4,531 

4,981 

5,644 

6,639 

8,256 

11,310 

18,978 

26.0 

3,842 

3,954 

4,128 

4,370 

4,711 

5,178 

5,868 

6,902 

8,584 

11,758 

19,731 

26.5 

3,991 

4,109 

4,288 

4,539 

4,892 

5,380 

6,095 

7,169 

8,917 

12215 

20,497 

27.0 

4,144 

4,266 

4,451 

4,712 

5,080 

5,585 

6,328 

7,443 

9,257 

12,680 

21,277 

27.5 

4,298 

4,425 

4,617 

4,888 

5,270 

5,793 

6,564 

7,721 

9,603 

13,153 

22,072 

28.0 

4,456 

4,588 

4,786 

5,068 

5,464 

6.006 

6,805 

8,005 

9,956 

13,637 

22,881 

28.5 

4,616 

4,753 

4,958 

5,250 

5,661 

6,223 

7,050 

8,292 

10,314 

14,128 

23,706 

29.0 

4,779 

4,921 

5,134 

5,436 

5,860 

6,443 

7,300 

8,586 

10,680 

14,627 

24,546 

29.5 

4,946 

5,093 

5,313 

5,626 

6,064 

6,667 

7,555 

8,885 

11,052 

15,136 

25,399 

30.0 

5,115 

5,267 

5,495 

5,818 

6,272 

6,895 

7,813 

9,189 

11,429 

15,654 

26,268 

30.5 

5,287 

5,444 

5,680 

6,014 

6,482 

7,127 

8,076 

9,497 

11,813 

16,181 

27,150 

31.0 

5,462 

5,624 

5,868 

6,213 

6,697 

7,363 

8,342 

9,811 

12,203 

16,715 

28,047 

31.5 

5,639 

5,806 

6,058 

6,414 

6,914 

7,602 

8,613 

10,130 

12,600 

17,259 

28,958 

32.0 

5,820 

5,992 

6,252 

6,619 

7,136 

7,845 

8,889 

10,455 

13,004 

17,811 

29,885 

32.5 

6,003 

6,180 

6,449 

6,828 

7,360 

8,092 

9,169 

10,784 

13,413 

18,372 

30,826 

33.0 

6,189 

6,372 

6,649 

7,040 

7,589 

8,343 

9,453 

11,119 

13,829 

18,941 

31,782 

33.5 

6,378 

6,567 

6,852 

7,255 

7,821 

8,598 

9,742 

11,458 

14,251 

19,520 

32,753 

34.0 

6,570 

6,764 

7,057 

7,472 

8,055 

8,856 

10,034 

11,802 

14,680 

20,105 

33,738 

34.5 

6,764 

6,964 

7,266 

7,693 

8,294 

9,118 

10,331 

12,151 

15,115 

20,701 

34,738 

35.0 

6,962 

7,168 

7,479 

7,919 

8,537 

9,385 

10,634 

12,506 

15,557 

21,307 

35,754 

35.5 

7,162 

7,374 

7,694 

8,147 

8,783 

9,655 

10,940 

12,865 

16,004 

21,921 

36,782 

36.0 

7,366 

7,584 

7,913 

8,378 

9,032 

9,929 

11,250 

13,230 

16,458 

22,542 

37,826 

36.5 

7,572 

7,796 

8,134 

8,612 

9,284 

10,206 

11,565 

13,601 

16,919 

23,172 

38,884 

37.0 

7,780 

8,011 

8,359 

8,850 

9,540 

10,482 

11,883 

13,977 

17,386 

23,812 

39,958 

37.5 

7,991 

8,229 

8,585 

9,090 

9,799 

10,773 

12,206 

14,356 

17,857 

24,461 

41,045 

38.0 

8,206 

8,450 

8,816 

9,334 

10,062 

11,062 

12,535 

14,742 

18,337 

25,116 

42,148 

38.5 

8,424 

8,674 

9,050 

9,582 

10,329 

11,356 

12,867 

15,133 

18,823 

25,781 

43,266 

39.0 

8,644 

8,900 

9,286 

9,832 

10,599 

11,652 

13,203 

15,528 

19,315 

26,455 

44,398 

39.5 

8,867 

9,130 

9,526 

10,086 

10,873 

11,952 

13,544 

15,929 

19,814 

27,137 

45,545 

40.0 

9,093 

9,363 

9,769 

10,343 

11,150 

12,258 

13,889 

16,335 

20,319 

27,829 

46,699 

40.5 

9,322 

9,598 

10,014 

10,603 

11,430 

12,567 

14,236 

16,745 

20,829 

28,529 

47,873 

41.0 

9,554 

9,836 

10,263 

10,867 

11,714 

12,879 

14,590 

17,163 

21,346 

29,238 

49,062 

41.5 

9,788 

10,078 

10,515 

11,133 

12,002 

13,195 

14,950 

17,584 

21,870 

29,955 

50,265 

42.0 

10,025 

10,322 

10,770 

11,403 

12,293 

13,515 

15,313 

18,010 

22,401 

30,682 

51,483 

42.5 

10,266 

10,569 

11,028 

11,677 

12,587 

13,838 

15,679 

18,441 

22,937 

31,417 

52,716 

43.0 

10,509 

10,819 

11,289 

11,953 

12,885 

14,166 

16,049 

18,877 

23,480 

32,160 

53,963 

43.5 

10,754 

11,072 

11,553 

12,233 

13,186 

14,497 

16,425 

19,319 

24,029 

32,912 

55,225 

44.0 

11,003 

11,329 

11,821 

12,516 

13,492 

14,833 

16,805 

19,766 

24,586 

33,674 

56,506 

218 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  37 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  CUT  ON 

SLOPING  GROUND 

Side  Slopes  2  to  1 


4 
t»$ 

ante 

aS.s 

SURFACE  SLOPE  OF  GROUND  IN  PER  CENT 

10 

15 

20 

25 

30 

35 

40 

45 

0.5 

2 

2 

2 

3 

3 

4 

5 

10 

1.0 

7 

8 

8 

9 

11 

14 

20 

38 

1.5 

18 

19 

20 

23 

26 

33 

47 

87 

2.0 

31 

33 

36 

40 

47 

58 

83 

156 

2.5 

48 

51 

55 

61 

72 

90 

128 

244 

3.0 

70 

74 

80 

89 

104 

131 

186 

352 

3.5 

95 

100 

109 

121 

142 

178 

252 

479 

4.0 

124 

131 

142 

158 

186 

233 

330 

623 

4.5 

157 

165 

179 

200 

235 

294 

417 

788 

5.0 

193 

203 

221 

247 

289 

363 

514 

972 

5.5 

233 

246 

267 

299 

350 

439 

622 

1,176 

6.0 

278 

293 

318 

356 

417 

523 

741 

1,400 

6.5 

326 

344 

373 

417 

489 

614 

869 

1,643 

7.0 

378 

399 

432 

484 

568 

712 

1,008 

1,906 

7.5 

434 

458 

496 

556 

652 

817 

1,158 

2,189 

8.0 

493 

521 

564 

632 

741 

929 

1,317 

2,491 

8.5 

557 

588 

637 

713 

837 

1,049 

1,486 

2,819 

9.0 

625 

659 

715 

800 

938 

1,176 

1,667 

3,160 

9.5 

697 

735 

797 

892 

1,046 

1,312 

1,857 

3,521 

10.0 

772 

814 

883 

988 

1,159 

1,453 

2,058 

3,903 

10.5 

851 

897 

973 

,089 

1,278 

1,601 

2,269 

4,304 

11.0 

933 

984 

1,067 

,095 

1,401 

1,754 

2,489 

4,722 

11.5 

1,020 

1,076 

1,167 

,307 

1,532 

1,920 

2,721 

5,162 

12.0 

1,111 

1,172 

1,270 

,423 

1,668 

2,091 

2,963 

5,621 

12.5 

1,205 

1,271 

1,377 

,543 

1,810 

2,268 

3,215 

6,099 

13.0 

1,304 

1,375 

1,490 

1,669 

1,959 

2,453 

3,478 

6,597 

13.5 

1,406 

1,483 

1,507 

1,800 

2,112 

2,644 

3,750 

7,113 

14.0 

1,513 

1,595 

1,729 

1,936 

2,271 

2,846 

4,033 

7,649 

14.5 

1,662 

1,711 

1,854 

2,076 

2,436 

3,053 

4,325 

8,203 

15.0 

1,736 

1,832 

1,985 

2,223 

2,608 

3,268 

4,630 

8,779 

15.5 

1,854 

1,956 

2,119 

2,374 

2,784 

3,489 

4,944 

9,378 

16.0 

1,975 

2,084 

2,257 

2,529 

2,966 

3,718 

5,268 

8,986 

16.5 

2,101 

2,217 

2,401 

2,690 

3,155 

3,954 

5,603 

10,625 

17.0 

2,230 

2,353 

2,549 

2,856 

3,349 

4,197 

5,946 

11,282 

17.5 

2,364 

2,493 

2,701 

3,027 

3,549 

4,448 

6,302 

11,954 

18.0 

2,500 

2,637 

2,857 

3,202 

3,754 

4,706 

6,667 

12,645 

18.5 

2,641 

2,785 

3,018 

3,382 

3,965 

4,971 

7,043 

13,358 

19.0 

2,785 

2,938 

3,183 

3,568 

4,183 

5,243 

7,429 

14,091 

19.5 

2,934 

3,095 

3,353 

3,759 

4,406 

5,621 

7,825 

14,842 

20.0 

3,087 

3,255 

3,527 

3,953 

4,634 

5,809 

8,231 

15,613 

20.5 

3,243 

3,420 

3,706 

4,151 

4,869 

6,103 

8,648 

16,403 

21.0 

3,403 

3,589 

3,889 

4,356 

5,109 

6,405 

9,075 

17,213 

21.5 

3,567 

3,762 

4,076 

4,565 

5,355 

6,713 

9,512 

18,042 

22.0 

3,734 

3,939 

4,268 

4,780 

5,608 

7,029 

9,959 

18,891 

22.5 

3,906 

4,120 

4,464 

5,000  '  5,866 

7,352 

10,417 

19,760 

STRUCTURAL  DIAGRAMS   AND    TABLES 


219 


TABLE  37  (Concluded) 

AMOUNT  OF  MATERIAL  IN  CUBIC  YARDS  PER  100  LINEAR  FEET  OF  CUT  ON 

SLOPING  GROUND 

Side  Slopes  2  to  1 


Depth  of 
Center  Cut, 
in  Feet 

SURFACE  SLOPE  OF  GROUND  IN  PER  CENT 

10      15 

20 

25 

30 

35 

40 

45 

23.0 

4,082 

4,306 

4,665 

5,225 

6,130 

7,683 

10,886 

20,648 

23.5 

4,262 

4,495 

4,879 

5,454 

6,399 

8,021 

11,364 

21,555 

24.0 

4,445 

4,688 

5,080 

5,689 

6,675 

8,365 

11,853 

22,482 

24.5 

4,631 

4,885 

5,293 

5,928 

6,955 

8,715 

12,352 

23,428 

25.0 

4,823 

5,087 

5,512 

6,174 

7,242 

9,075 

12,861 

24,395 

25.5 

5,018 

5,292 

5,734 

6,424 

7,533 

9,442 

13,380 

25,381 

26.0 

5,216 

5,500 

5,960 

6,678 

7,830 

9,817 

13,909 

26,385 

26.5 

5,419 

5,714 

6,192 

6,938 

8,135 

10,199 

14,450 

27,410 

27.0 

5,625 

5,932 

6,428 

7,202 

8,445 

10,587 

15,000 

28,454 

27.5 

5,835 

6,154 

6,669 

7,471 

8,762 

10983 

15,561 

29,518 

28.0 

6,049 

6,380 

6,813 

7,746 

9,083 

11,386 

16,132 

30,600 

28.5 

6,268 

6,611 

7,163 

8,027 

9,411 

11,798 

16,714 

31,704 

29.0 

6,490 

6,845 

7,417 

8,311 

9,744 

12,215 

17,305 

32,826 

29.5 

6,715 

7,083 

7,674 

8,598 

10,082 

12,638 

17,906 

33,967 

30.0 

6,945 

7,328 

7,937 

8,891 

10,428 

13,071 

18,519 

35,129 

30.5 

7,178 

7,572 

8,204 

9,188 

10,779 

13,510 

19,141 

36,309 

31.0 

7,415 

7,821 

8,475 

9,491 

11,135 

13,954 

19,773 

37,509 

31.5 

7,657 

8,075 

8,750 

9,801 

11,497 

14,410 

20,417 

38,729 

32.0 

7,902 

8,333 

9,030 

10,115 

11,865 

14,871 

21,071 

39,968 

32.5 

8,150 

8,596 

9,314 

10,434 

12,238 

15,339 

21,735 

41,227 

33.0 

8,403 

8,863 

9,603 

10,758 

12,617 

15,815 

22,409 

42,506 

33.5 

8,660 

9,133 

9,896 

11,086 

13,002 

16,298 

23,093 

43,803 

34.0 

8,920 

9,408 

10,194 

11,419 

13,393 

16,788 

23,787 

45,120 

34.5 

9,184 

9,687 

10,496 

11,757 

13,791 

17,286 

24,492 

46,457 

35.0 

9,452 

9,970 

10,802 

12,100 

14,194 

17,791 

25,207 

47,813 

35.5 

9,724 

10,257 

11,113 

12,447 

14,602 

18,302 

25,932 

49,189 

36.0 

10,000 

10,548 

11,429 

12,800 

15,016 

18,820 

26,668 

50,585 

36.5 

10,280 

10,843 

11,749 

13,158 

15,436 

19,346 

27,414 

52,000 

37.0 

10,563 

11,142 

12,073 

13,522 

15,861 

19,880 

28,170 

53,434 

37.5 

10,850 

11,445 

12,401 

13,891 

16,293 

20,422 

28,937 

54,888 

38.0 

11,142 

11,752 

12,733 

14,264 

16,730 

20,971 

29,713 

56,361 

38.5 

11,437 

12,063 

13,071 

14,642 

17,174 

21,527 

30,500 

57,855 

39.0 

11,737 

12,378 

13,413 

15,025 

17,623 

22,190 

31,297 

59,368 

39.5 

12,039 

12,697 

13,759 

15,413 

18,078 

22,660 

32,104 

60,906 

40.0 

12,346 

13,021 

14,110 

15,805 

18,539 

23,237 

32,923 

62,451 

40.5 

12,656 

13,349 

14,465 

16,202 

19,006 

23,821 

33,752 

64,021 

41.0 

12,971 

13,681 

14,824 

16,605 

19,479 

24,414 

34,590 

65,611 

41.5 

13,290 

14,017 

15,187 

17,013 

19,957 

25,012 

35,438 

67,221 

42.0 

13,612 

14,357 

15,556 

17,425 

20,441 

25,619 

36,298 

68,851 

42.5 

13,938 

14,701 

15,929 

17,842 

20,930 

26,231 

37,168 

70,501 

43.0 

14,267 

15,049 

16,306 

18,264 

21,424 

26,852 

38,047 

72,170 

43.5 

14,601 

15,401 

16,687 

18,691 

21,925 

27,481 

38,937 

73,588 

44.0 

14,939 

15,757 

17,073 

19,124 

22,432 

28,116 

39,837 

75,565 

220  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

Retaining  Walls  and  Beams. — Retaining  walls  and  beams 
play  a  very  important  part  in  the  design  of  irrigation  structures. 
A  simple  graphical  method  of  calculating  earth  pressures  on 
retaining  walls  is  described  by  Prof.  William  Cain  in  the  Trans- 
actions of  the  American  Society  of  Civil  Engineers  of  June, 
1911,  from  which  the  following  is  taken: 


R    C  D       Ground  Surface 

ssss-s 


(1)  A  F  P  G  is  a  wall  of  any  shape  or  dimensions. 

(2)  <f>  =  Angle  of  repose  of  material. 

(3)  <£'  =  Angle  of  friction  between  material  and  wall. 

(4)  F  R  D  is  the  ground  surface. 

(5)  Draw  RA. 

(6)  Produce  D  R. 

(7)  Draw  F  B  parallel  to  RA. 

(8)  Draw  B  O  parallel  to  A  Y. 

(9)  Describe  the  arc  A  M  D  on  A  D. 

(10)  Draw  0  M  J_  to  A  D. 

(11)  With  A  as  center,  describe  arc  M  I. 

(12)  Draw  /  C  parallel  to  A   Y. 

(13)  Make  /  L  =  I  C  and  draw  C  L. 

(14)  The  total  pressure  on  one  linear  foot  of  wall  is  then 

equal  to  the  area  of  the  triangle  I  C  L  multiplied 
by  the  weight  of  1  cubic  foot  of  the  material. 

(15)  The  point  of  application  may  be  taken  as  at  one- third 

A  F  from  A.  The  average  pressure  equals  the  total 
divided  by  A  F.  The  maximum  pressure  equals 
twice  the  average. 

(16)  When  R  D  is  parallel  to  A  D  the  formula  for  total 

pressure  on  A  F  is : 


STRUCTURAL  DIAGRAMS   AND   TABLES  221 

e  —  wt.  of  1  cu.  ft.  of  material 

h  =  height  of  wall 

See  Fig.  45  for  total  earth  pressures  on  walls  without  sur- 
charge based  on  equivalent  water  pressure. 

Formulas  for  Maximum  Bending  Moments  in  Beams. — 
The  variation  of  pressures  on  any  submerged  wall  due  to 
water  or  earth  is  generally  triangular  or  trapezoidal,  that  is, 
the  loading  at  one  end  is  greater  than  at  the  other.  In  the 
following  list  are  given  the  principal  formulas  for  calculating 
the  bending  moments  due  to  uniform  loads,  triangular  loads, 
and  trapezoidal  loads.  The  bending  moments  are  given  in 
inch-pounds;  the  loading  is  in  pounds  per  linear  foot;  and  the 
span  is  in  feet. 

Uniform  loading: 

W  =  load  on  beam  in  pounds  per  linear  foot. 

/  =  span  in  feet. 
M  =  bending  moment  in  inch-pounds. 

(1)  M  =  1.5  W  I2,  for  a  simple  beam. 

(2)  M  =  W  I2,  for  negative  bending  moment  at  the  supports 

of  a  fixed  beam. 

(3)  M  =  0.5  W  I2  for  the  positive  bending  moment  at  the 

center  of  a  fixed  beam. 

(4)  M  =  6  W  I2,  for  a  cantilever  beam. 

Triangular  loading: 

P  =  load  at  end  of  beam  in  pounds  per  linear  foot. 

(5)  M  =  0.77  P  I2,  for  a  simple  beam. 

(6)  M  =  0.6  P  I2,  for  the  maximum  negative  bending  mo- 

ment at  the  more  heavily  loaded  end  of  a  fixed 
beam. 

(7)  M  =  0.26  P  I2,  for  the  maximum  positive  bending  mo- 

ment between  supports  of  a  fixed  beam. 

(8)  M  =  2  P  I2,  for  a  cantilever  beam  having  the  base  of 

triangular  load  at  supported  end. 

Trapezoidal  loading: 

Wi  =  load  in  pounds   per   linear  foot  at  lightly 
loaded  end. 


222  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

PI  =  load  in  pounds  per  linear  foot  at  heavily 
loaded  end. 


(9)    M  =         (/*  -  x*}  +  -j  (P,  -  IF:)    (l  -  |) 


for 


simple    beam,  the  point  of    maximum    bending 
moment  being  at 


(10)  M  =  Wi  I2  +  0.6  (Pi  -  Wi)  I2,  for  the  maximum  nega- 

tive moment  at  the  heavily  loaded  support  of  a. 
fixed  beam. 

(11)  M  =  0.5  Wi  I2  +  0.26  (Pl  -  Wi)  /2,  for  the  maximum 

positive  (approximate)  moment  between  supoorts; 
of  a  fixed  beam. 

(12)  M  =  6  Wi  I2  +  2  (Pi  -  Wi)  I2,  for  cantilever  beams, 

with  the  heavier  loading  at  the  supported  end. 

Table  38  gives  the  bending  moments  in  thousands  inch- 
pound  units  in  beams  one  foot  wide  for  triangular  loading,  that 
is:  for  loads  varying  uniformly  from  0  pounds  per  linear  foot  at 
one  end  to  P  pounds  per  linear  foot  at  the  other  end,  due  to 
water  and  earth  pressures.  <£  is  the  angle  of  repose  of  the  earth 
and  6  is  the  slope  of  surface  of  ground  back  of  the  wall.  The 
face  of  the  wall  against  which  the  pressure  acts  is  assumed  to  be 
vertical  and  the  angle  of  friction  between  earth  and  wall  is  not 
considered. 

Formulas  for  Reinforced  Concrete  Design.  —  The  theory  of 
the  design  of  a  rectangular  concrete  beam  reinforced  on  one  side 
may  be  illustrated  by  the  following  diagram  : 


Any  section  A-B  of  a  reinforced  concrete  beam  subjected  to 
a  bending  moment  has  acting  on  it  the  forces  P,  representing 
the  total  stress  in  the  steel,  and  PI,  representing  the  total 


STRUCTURAL  DIAGRAMS   AND   TABLES 


223 


O 

|8 

r^       « 
P 

o  Q 

f    Q 


§  i 


111 

w  P  O 

CQ    O  w 


O    O    S 
S5    H    ft 


55  2 

O    H 


§  3  o 

H  w  U 


M  «      P 

g  W    en 

,  PH    en 

CM  u 

g  |fi 

^  O    H 

Sow 


§ 

i 

igsi 

siiii 

a 

1 

llll 

os  os  o  w  •<* 

•*  t-  rH  10  CD 
rH  rH  d  W  CO 

00 

ca 

rH  rH  N  CO 

t-  d  OS  rji  OS 
W  10  t-  rH  0 
rH  rH  rH  d  CO 

t- 

rH 

i 

00  Tj«  rH  VO 
Tj<  CO  00  0 
rH  rH  rH  CO 

ISSli 

s 

s 

CO  t-  rH  •*)< 

SSSS 

CO 
rH  rH  rH  d 

IO 

S 

2233 

rH  rH  rH  d 

10  00 

rH 

§ 

rH   rH 

00  Tj<  rH 
S*  rH  Tl*  rH  IO 
t-  00  0  rj< 
rH  rH 

CO 
rH 

1 

rH  W   O 

CO  CO  rH  (O 

•   <o  i?  oo  co 

rH 

OS  W  CO  t-; 

rH 

rH 

8 

0  CO  t-; 

CD  O  OS  10  CD 

J2 

1 

rH 

o 

3 

r-J  **  rH  fr- 

O  CO  00  OS  CD 

ri23$S 

o    "«3  .2 

«  'M 

0 

H 

rH 
00 

rHCOOSrH 
0  CO  CO  <N 

CO  CO  CO  <O 

00  O  CD  t-  O 
rH   CD*  0  CD  CO 
(N  W  CO  CO  iO 

g  i  i 
l  *  ^ 

. 

rH 

id 

CO 

OS  CO  OS  CO 

OS  O  CO  00  l> 

io'  os  IN'  CD  06 

rH   rH   (M   W   CO 

03     .2   -J3 

*  §E 

fl       Jj    J^ 

00 

to 

Tl-rHOSOO 
U5  t-  00  rH 
rH  rH  rH  CO 

rH  CO  t-  00  rH 
r-i  CO  IO'  00  t-* 
rH   rH   rH   rH  C<I 

111 

«<•«*£ 

t- 

2 

CO  ^jj  «0  CO 

10  05   10   CD  W 
t>  00  0  (N*  00 
rH  rH  rH 

^    ^    ° 

III 

. 

d 

rH 

10  (N  0  TH 

50  t-  00  CO 

rH 

t>  CD  CD  OS  10 
•*  10  CD*  t-*  rH 

1     I! 

oj      i-«     en 

°    'S'o 

„• 

. 

0 

00  N  «0  00 

co*  •*  r)5  t> 

t>  CO  00  CO  CD 
C<3  CO  CO  "tf  CO 

g  -as. 

S  - 

1 

* 

rH 

CO 

OS  rH  CO  0 

•^  t-  q  co  ^J 

rH  rH  N  W  CO 

^      «J    « 

i  "  " 

o 

"     / 

tn 

o 

/ 

X 

10 

XXXX 

rH  CO  OS  t- 

xxxxx 

CO  OO  00  t-  OS 

<u 

3 

0 

X 
& 

/'** 

f 

OS  CO  t-  O 
CO  •<*  ^  00 

00  CO  OS  t>  00 
<N  CO  CO  Tf  CO 

-2 

U3 

IS 

OH 

|ce 

| 

rt 

IJI  1 

o     O  CO  O  % 
0  N  <N  CO  CO 

II      II      II     II     II 

1 

J3 

d 

0 

tn 

s7s 

|f| 

B 

3 

224 


WORKING  DATA   FOR   IRRIGATION  ENGINEERS 


£ 

-e 
i- 

H 


"5 


s? 


I  O  10  CO  10  CO  rH 

-      8SS583 


t-  rH  00 
CO  IO  5C 
rH  rH  rH  < 


2  2  2  S 

5<  rt  10  00 


*  CO  CO  00 
>  Oi  rH  IO 
H  rH  eg  CO 


o  co  oo  oo 

M  <N  (N  ^f 


OCOt>00 


rH  t>  CO  CD 

id  id  cd  d 


rH  CO  CO  10 

kdiocod 


Tf  CO  CD  kO 
CO  O  O5  rH  CO 
Tf  10  10  t-  0 


O  CD  t-  00  CO  10  CO  t>  CO  rH 

rH  O  O  O  rH  O  O  O  O  rH 


xxxx 


rH  CO  05  t-_ 

05  co  t-  d 

CO    T}<    T}«    CO 


O  rH 


CO  rH  00 

S*  eo  t~  t-  as 
00  05  rH  CO 


00  CO  O5  CO 
05  10  r^  0 
CO  CO  T*  10 


CD  CD  IO  IO 

CD  id  id  06  eo 

Tf  10  CD  C-  rH 


O  OO  rH  CO  CO 


eoeeeio^i 

O5  IO   rH  O5  rH 
CO  CO  •*  Tf   C- 


CO  0  t-  CO  CO 
CO  >0  t>  rH  0 

rH  rH  rH  CO  CO 


q  co  05  co  TJ; 


CO  t-  CO 
t>  CO  O 


b-.  -*  CO  t>  CO 


t-.  Tf  CO  CO  rH 
CO  Tf  10  CO  O5 


CO  O5  CO  CO  CO 
rH  rH  CO  CO  CO 


lOt^COrH  rHCOlOOOCO 

rHrHrHCO  rHrHrHrHCO 


xxxxx 

CO  OO  00  t>  O5 


CO  Tj«  t-  t- 

S  05  10  0 
10  CO  rH 


CO  IO  O5 
10  0  10 


<  CO  rH  CO 
CO  t-  05 


alss 


Tf  10  00  10 
O  rH  CO  rH 
rH  rH  rH  CO 


O  rH  00 
t>  CO  05  00 
10  CO  CD  rH 


qcoqco 

0  Tl«  05  CO 

Tf    Tf    Tf    00 


coooqca 


OlOrHCO 
10  10  CD  0 


xxxx 


rH  CO  Cft  t^ 
05  CO  l>  O 


O  rH  CO 

1!    II    II 


SrH  t-  Tl<  CO 
-*  CO  CD  0 
rl«  IO   CD  t-  rH 


co  Tf  10 
-^r  10  Ti< 

10  CO  05 


i 
C~  CO  O5  CD  IT- 

CO  CO  CO  ••t  CD 


t-  CD  rH 
t-  CO  O5 
CO  CO  CO 


rH  00  05  CO  10 
O5  CO  CO  CO  CD 
rH  CO  CO  CO  Tjt 


SSSa 


-q 

IO  O  CD  C-  ^< 
t-  05  0  CO  00 


CO  CO  CO  Tf 

cd  t>  oi  id  oo 

IO  CD  t-  O5  CO 


eocoqio 


O  CO  t-  00  10 

05  TJ!  d  06  d 

CO  CO  •*!•  •*  t- 


•^  CO  CO  t>  CO 
O5  CO  t>  CO  t- 

rH  CO  CO  CO  •* 


rH  10  05  05  CO 
t>  00  05  rH  t^ 


CO  COrH  rH 
CO  •*  10  CD 


XXXXX 


CO  00  CO  t>  05 

06  eo  OJ  t>  06 

CO  CO  CO  -^  CO 


o     O  CO  O  ^t 

o  co  co  n  so 
II    II    II    II    II 


- 


STRUCTURAL  DIAGRAMS  AND   TABLES  225 

stress  in  the  concrete.  The  stress  in  the  steel  is  concentrated 
at  one  point,  but  the  compressive  stress  in  concrete  (tensile 
stress  from  C  to  B  is  neglected,  as  it  has  no  influence  on  the 
ultimate,  or  even  the  working  strength  of  the  beam)  varies  from 
zero  at  C  to  a  maximum  at  A ,  the  rate  of  increase  being  uniform 
from  C  to  A .  The  summation  of  these  stresses  is  represented  by 
pl  =  pt  whose  point  of  application  is  one-third  of  A  C  below  A . 
The  resisting  moment  of  the  section,  therefore,  is  equal  to  P  x 
or  PI  x,  and  this  must  be  equal  to  the  bending  moment,  or  M  = 
P  x  =  Pi  x. 

The  value  of  x  for  a  given  beam  depends  upon  the  location  of 
the  neutral  axis  which  varies  with  different  percentages  of  steel 
and  with  the  quality  of  the  concrete.  This  variation  is  slight 
for  ordinary  percentages  of  steel  and  grades  of  concrete  used  in 
practice  and  the  neutral  axis  may  be  assumed  to  be  located  at 
0.39  d  below  the  top  of  the  beam.  The  point  of  application  of 

PI,  then,  is  -^-r—  =  0.13  d  below  the  top  of  the  beam  and  the 

lever  arm  x  of  internal  stresses  is  d  —  .13  d  —  .87  d,  or  J/%  d, 
and  the  resisting  moment  is  %  d  P. 
Therefore,  M  =  .7/s  d  P 

and  P  =  -=-r  =  Pi 

If  f8  represents  the  intensity  of  working  stress  in  the  steel, 
the  area  of  steel  required  is 

*.,,**. 

'  /.  "Idf. 

The  shifting  of  the  neutral  axis  has  a  greater  influence  on 
the  fiber  stress  in  the  concrete  than  on  the  stress  in  the  steel. 
On  the  assumption  that  the  coefficient  of  elasticity  of  concrete 
is  equal  to  2,000,000,  which  corresponds  to  a  good  grade  of  con- 
crete, the  position  of  neutral  axis  will  vary  from  .3  d  to  .48  d 
below  the  top  of  beam  for  percentages  of  steel  varying  from  0.4 
to  1.5,  the  ordinary  range  of  practice. 

With  this  variation  in  the  position  of  the  neutral  axis,  the 

maximum  fiber  stress  in  the  concrete  varies  from  fc  —    ' 


226  WORKING   DATA   FOR   IRRIGATION  ENGINEERS 

for  0.4  per  cent  steel  to/c  =  -r~   for  1.5  per  cent  steel.    These 


equations  apply  only  to  working  stresses  of  about  one-fourth  the 
ultimate.  Beyond  this  point  the  variation  of  stresses  in  the 
concrete  becomes  parabolic,  resulting  in  a  different  set  of  equa- 
tions. 

For  approximate  design,  Turneaure  and  Maurer  give  the 
following  formulas: 

M  =  bending  moment  in  inch-pounds 

/,  =  unit  stress  in  steel 

fc  =  maximum  fiber  stress  in  concrete 

b  =  width  of  beam 

d  =  depth  of  beam  above  plane  of  steel 

p  =  ratio  of  steel  area  to  concrete  area  =  7—: 

bd 

for         p    =  %6j- 

~     ?f  8  P     3  ft 

If  a  value  of  p  greater  than  &  -f  is  used,  then  equation  (2) 

/* 

should  be  used  to  determine  b  and  d.  If  a  value  of  p  less  than 
&  y  is  used,  equation  (l)  should  be  used  for  determining  b  and  d. 

Js 

If  equation  (2)  is  used,  the  unit  stress  in  the  steel  is  given  very 
closely  by  equation  (1)  in  all  cases,  but  if  equation  (1)  is  used 
for  determining  b  and  d  equation  (2)  will  not  give  the  unit  stress 

in  the  concrete  unless  p  =  /(6  ~.    For  other  values  of  p  the  unit 

Js 

7.5M 
stress  in  the  concrete  may  range  approximately  from  fc  =    ,   ,2 

for  p  —  0.4  per  cent  to  fc  =  -7-^  for  p  =  1.5  per  cent. 


STRUCTURAL  DIAGRAMS  AND   TABLES  227 

Example  of  Use  of  Above  Formulas. — A  concrete  beam  has  a 
bending  moment  of  50,000  inch-pounds,  /,  is  to  be  not  greater 
than  12,000  and  fc  is  to  be  not  greater  than  500.  Determine  b 
and  d  and  the  area  of  steel  required.  In  order  to  have  /,  =  12,000 
and/c  =  500, 

.  _  s/    fc  _  s/    x   5,000 

P  "    /16  /    —    /16  X   10  nnn   —    .UU/S 

=   0.78  per  cent. 


From  (2)      b  d?  =  -  -^^  -  =  600 

If  b    =  8  inches  d  =  A  —  =  8.7  inches 


Now,  if  it  were  desired  to  use  1.00  per  cent  of  steel,  equation 
(2)  would  be  used  and  we  would  have  b  dz  equal  to  600  as  before, 
while  the  stress  in  the  concrete  would  be  between  500  and  410, 

\  =  TTdv  or  rou&hly>  470,*  and  the  stress  in  the  steel  would  be 

•    _    _8M_,          8X50,000 
J*~  7pbd2  "  7X  .01  X  600 

If  only  0.5  per  cent  steel  were  used,  equation  (1)  would  be 
used  for  finding  b  and  d: 

8  X  50,000 
=  7  X  12,000  X  .005  = 


If  b  =  8     d  =  \          =  11  inches 


*  The  stress  of  500  corresponds  to  a  percentage  of  steel  of  .78  and  410 
(  =  b~d?  )  corresponds  to  a  percentage  of  1.5  as  above  stated.  The  assumption 
of  a  linear  variation  between  these  limits  gives  a  stress,  corresponding  to  1.0 
per  cent  steel,  of  500  -  f^  (500  -  410)1  =  470  pounds  per  square  inch. 


228  WORKING   DATA  FOR  IRRIGATION  ENGINEERS 

In  this  case,  the  stress  in  the  steel  would  be  12,000  pounds  per 
square  inch,  as  assumed,  but  the  stress  in  concrete  would  be 

,  7.5  M       7.5  X  50,000 

between  500  and    ,   ,2    =  -  :rr^  --  =  395;  in  fact,  it  would 
o  (t  " 


be  very  near  the  latter  figure  —  roughly,  370. 

By  means  of  the  above  equations,  approximate  calculations 
can  be  rapidly  made  without  the  use  of  tables,  diagrams,  or  com- 
plicated formulas,  and  they  will  be  found  to  serve  admirably  for 
ordinary  beam  problems  when  tables  or  diagrams  are  not  avail- 
able. 

Fig.  40*  is  a  convenient  diagram  for  proportioning  rein- 
forced concrete  beams.  This  diagram  is  based  on  a  ratio  of 
coefficient  of  elasticity  of  steel  to  coefficient  of  elasticity  of 
concrete  of  15.  Its  values  correspond  closely  with  those  ob- 
tained from  the  above  equations. 

Table  39  *  for  round  rods  and  Table  40  *  for  square  rods  are 
convenient  for  use  with  this  diagram  in  the  design  of  walls  and 
slabs. 

Illustrative  Examples.  —  The  bending  moment  M  in  a  beam 
is  50,000.  Find  the  values  of  b,  d,  and  p  required  to  carry  this 
when  fc  =  400  and  /,  =  10,000  :  Solution  :  At  the  intersection 
of  the  lines  marked  fc  =  400  and  f8  =  10,000  we  read  the 

percentage  of  steel  equals  0.75  and  M  Ib  d2  =  65  .*.  b  d2  =  —  = 

bo 

770.     If  b  =  8  inches,  d  =  -y  —  =  9.8  inches  from  the  top  of 

beam  to  center  of  steel.       Area  of  steel  required  8  X  9.8  X 
.0075  =  0.59  square  inches,  requiring  2  J^-inch  round  rods. 

(2)  The  bending  moment  per  linear  foot  on  a  concrete  re- 
taining wall  is  75,000  inch-pounds.  Find  the  thickness  of  wall 
and  size  and  spacing  of  reinforcement  rods  required  when  /,  = 
12,000  and  fc  =  500.  Solution:  As  before  read  from  the  dia- 

gram T-p  =  84  and  p  =  0.8. 

M_  75,000 

b  d2  =  b  d2 

*  Reproduced  by  permission  from  "Principles  of  Reinforced  Construc- 
tion," by  Turneaure  and  Maurer,  John  Wiley  &  Sons,  New  York. 


STRUCTURAL  DIAGRAMS  AND   TABLES 


229 


FIG.  40. — Coefficients  of  Resistance  of  Reinforced  Concrete  Beams. 

R   -   M 

R  ~bd2 


230 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


I 


CQ 


T-H    ^H    i-l    <N 


.     t-   »N  i-"  c« 


_      r_      ^     rH     C^      (N     CO 


i—  iC^(N-^4OOOOOiT-HCOCOOOOO(NO5t^- 


COCOCO(N^O5l>00(NOOOOT-<t^l>O5(NOO 
C^CO»Ol>Oir-Hrtll>T-I^JHOOCOI>-I>OOi—  1    ^ 

^-i   ^H'   ^i   <M'   (N   (N   CO   CO   ^   O  l>   00 


IIS 


00   O 


i—  i(NCOiO 


'Tt)cOOcDTt|Tt|t>-OOI>-'^l 
O<NiOi>OCOCDCO'—  lO 


<N<NC^<N<NCOCOCO'<f^ 


Saipul     I       H-*  *&  «|oo  i 

•aziS 


STRUCTURAL  DIAGRAMS   AND   TABLES 
I. 


231 


W 


^     3 


X 


"Q   03 


'3ZIS 


T-H    rH    rH    rH    (N    (N 


(N   <N   CO 


<N    (N    CO 


<N   <N   CO  TJH   T^I 


r-    T-    i-    (N   (N   CO   CO 


I-HI—  ii—  I(M(NCOCO^»OCD1>'O5T-ICO 


^tlO'^HCOl>-iOCvflCDO5 
rH(MCOCO-^iOCOi>-OO 


»O 


232 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 
75,000 


.'.bd2 


Since  b  =  12,  d  = 


=  893 


8.6  inches 


Area  of  steel  per  foot  of  wall  12  X  8.6  X  .008  =  .83  square 
inch.     From-  Table  39  we  read  that  ^-inch  round  rods  spaced 
inches  on  centers  will  supply  this  area. 


TABLE  41 

QUANTITIES  OF  MATERIALS  REQUIRED  FOR  ONE  CUBIC  YARD   OF  RAMMED 
CONCRETE,  ASSUMING  A  BARREL  OF  3.8  CUBIC  FEET 


PARTS  IN  Mix 

Voros  IN  BROKEN  STONE  OR  GRAVEL 

45%* 

40  %t 

Cement 

Sand 

Stone 

Cement 

Sand 

Stone 

Cement 

Sand 

Stonet 

Bbl. 

Cu.   Yd. 

Cu.   Yd. 

Bbl. 

Cu.   Yd. 

Cu.   Yd. 

1 

2 

3H 

.68 

0.47 

0.83 

.61 

0.45 

0.79 

1 

2 

4 

.57 

0.44 

0.88 

.50 

0.42 

0.84 

1 

2 

4^ 

.48 

0.42 

0.94 

.41 

0.40 

0.89 

1 

2^ 

3 

.66 

0.58 

0.70 

.60 

0.56 

0.68 

1 

2^ 

3^ 

.55 

0.55 

0.76 

.49 

0.52 

0.73 

1 

2H 

4 

1.46 

0.51 

0.82 

.40 

0.49 

0.79 

1 

2^ 

4M 

1.37 

0.48 

0.87 

.31 

0.46 

0.83 

1 

2^ 

5 

1.30 

0.46 

0.92 

.24 

0.44 

0.87 

3 

5 

1.22 

0.52 

0.86 

.17 

0.49 

0.82 

3 

5^ 

1.16 

0.49 

0.90 

.11 

0.47 

0.86 

3 

6 

1.11 

0.47 

0.94 

.05 

0.44 

0.89 

4 

7 

0.92 

0.52 

0.91 

0.88 

0.50 

0.87 

4 

8 

0.85 

0.48 

0.96 

0.81 

0.46 

0.91 

*  For  broken  stone. 

t  For  gravel  or  stone  and  gravel. 

Timber  Structures. — Various  tables,  etc.,  are  given  in  the 
following  pages  which  may  be  found  useful  in  the  design  of 
timber  structures.  The  formulas  for  bending  moments  are 
given  on  page  221.  The  common  flexure  formula  for  beams  of 
any  shape  is: 

Me 
I 

where  S  =  stress  on  extreme  fiber  in  pounds  per  square  inch 
M  =  bending  moment  in  inch-pounds 
c  =  distance  from  neutral  axis  to  extreme  fiber  in  ins. 
7  =  moment  of  inertia  in  inches4 


STRUCTURAL  DIAGRAMS  AND  TABLES 


233 


TABLE  42 
ALLOWABLE  UNIT  STRESSES  AND  WEIGHTS  OF  TIMBER 


Kind  of  Timber 

Ten- 
sion 

COMPRESSION 

SHEARING 

Weight 
in 
Lbs. 
per 
Cubic 
Foot 
Dry* 

With  Grain 

Across 
Grain 

With 
Grain 

4 

Across 
Grain 

End 
Bear- 
ing 

Col- 
umns 
Under 
15 
Diams. 

Factor  of  Safety 

10 

5 

5 

4 

4 

White  oak 

1200 
700 
1200 
800 
900 
800 
800 

600 

600 
700 
850 
700 

1400 
1100 
1400 
1200 
1100 
1000 
1200 

1100 

1000 
1100 

1000 

800 
1000 
900 
800 
750 
900 

800 

750 
750 
800 
800 
800 

500 
200 
350 
200 
250 
200 
200 

150 

200 
200 
250 
150 

200 
100 
150 
130 
100 

ioo 

100 

ioo 

150 
100 

1000 

500 
1250 

iooo 

'756 

f 

600  | 

400 
500 

46.4 

25.6 
38.1 
32.1 
38.4 
30.2 
25.0 
26.4 
to 
32.3 
29.8 
23.1 
41.0 
26.2 
25.0 

White  pine  

Southern  long-leaf  pine  
Douglas  fir 

Short-leaf  yellow  pine  . 

Norway  pine 

Spruce  and  eastern  fir. 

Hemlock           

Cvoress 

v_y  p        
Cedar          

Chestnut  

Cal.  redwood  
Cal.  spruce  

*  The  weights  of  green  or  unseasoned  timbers  are  20  to  40  per  cent  greater. 

The  above  unit  stresses  are  recommended  by  the  Association  of  Railway 
Superintendents  of  Bridges  and  Buildings.  They  are  for  unseasoned  timber. 
For  structures  not  subjected  to  impact,  these  stresses  may  safely  be  increased 
25  per  cent. 

For  columns  having  a  length  greater  than  fifteen  times  the  least  dimen- 
sion, the  safe  end-bearing  stress  may  be  obtained  by  the  following  formula: 


when  Si  =  allowable  compression  in  column 
5  =  allowable  end-bearing  from  table 
L  =  length  of  column  in  feet 
d  =  least  side  of  column  in  inches 


234  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


<&     5 
g     o 

xi 


?s? 

&S- 

Q 


»-iC<l 


OCOOCOCOOCOCOOCOCOOO 


€§888888880000 

«  **  *  S  8  8  3  S  S  8  3  t 


SS  2  8  §8  ?  S 


S  g 


lOCOOCOCOOCOCOOCCCCOO 
t^*       CO       C^      CO       CO       ^^       CO       CO       ^D       CO       CO       ^^       ^^ 


(MCO(MO 


t^b-Ot^t>OO 

i-<cO»OcDi—  i      O      »O 

oodeo^o^i> 

i-l        rH        i-H        (N        C^        CO 


»O 
<N 


CO^OOOOCCDOO 


<M      <N      <N      CO 


STRUCTURAL  DIAGRAMS   AND   TABLES 


235 


TABLE  44 
CONTENTS  IN  FEET  B.M.  OF  LUMBER 


Size  of  Piece, 
Inches 

LENGTH,  IN  FEET 

10 

12 

14 

16 

18 

20 

22 

24 

2x  4 

6% 

8 

9% 

10% 

12 

13% 

14% 

16 

2x  6 

10 

12 

14 

16 

18 

20 

22 

24 

2x  8 

13H 

16 

18% 

21% 

24 

26% 

29% 

32 

2x10 

16% 

20 

23% 

26% 

30 

33% 

36% 

40 

2x12 

20 

24 

28 

32 

36 

40 

44 

48 

2x14 

23% 

28 

32% 

37% 

42 

46% 

51% 

56 

2x16 

26% 

32 

37% 

42% 

48 

53% 

58% 

64 

4x  4 

13H 

16 

18% 

21% 

24 

26% 

29% 

32 

4x  6 

20 

24 

28 

32 

36 

40 

44 

48 

4x  8 

26% 

32 

37% 

42% 

48 

53% 

58% 

64 

4x10 

33% 

40 

46% 

53% 

60 

66% 

73% 

80 

4x12 

40 

48 

56 

64 

72 

80 

88 

96 

4x14 

46% 

56 

65% 

74% 

84 

93% 

102% 

112 

6x  6 

30 

36 

42 

48 

54 

60 

66 

72 

6x  8 

40 

48 

56 

64 

72 

80 

88 

96 

6x10 

50 

60 

70 

80 

90 

100 

110 

120 

6x12 

60 

72 

84 

96 

108 

120 

132 

144 

6x14 

70 

84 

98 

112 

126 

140 

154 

168 

6x16 

80 

96 

112 

128 

144 

160 

176 

192 

8x  8 

53% 

64 

74% 

85% 

96 

106% 

117% 

128 

8x10 

66% 

80 

93% 

106% 

120 

133% 

146% 

160 

8x12 

80 

96 

112 

128 

144 

160 

176 

192 

8x14 

93% 

112 

130% 

149% 

168 

186% 

205% 

224 

10x10 

83% 

100 

116% 

133% 

150 

166% 

183% 

200 

10x12 

100 

120 

140 

160 

180 

200 

220 

240 

10x14 

116% 

140 

163% 

186% 

210 

233% 

256% 

280 

10x16 

133% 

160 

186% 

213% 

240 

266% 

293% 

320 

12x12 

120 

144 

168 

192 

216 

240 

264 

288 

12x14 

140 

168 

196 

224 

252 

280 

308 

336 

12x16 

160 

192 

224 

256 

288 

320 

352 

384 

14x14 

163% 

196 

228% 

261% 

294 

326% 

359% 

392 

14x16 

186% 

224 

261% 

298% 

336 

373% 

410% 

448 

236 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


TABLE  45 
CONTENTS  IN  FEET  B.M.  OF  LOGS 


Diam.  of 
Log,  Ins. 

LENGTH,  IN  FEET 

8 

10 

12 

14 

16 

18 

20 

22 

8 

8 

10 

12 

14 

16 

18 

20 

22 

9 

12MI 

16 

18 

22 

25 

28 

31 

34 

10 

18 

23 

27 

32 

36 

41 

46 

50 

11 

24^ 

31 

37 

43 

49 

55 

61 

67 

12 

32 

40 

48 

56 

64 

72 

80 

88 

13 

40^ 

50 

61 

71 

81 

91 

101 

111 

14 

50 

62 

75 

88 

100 

112 

125 

137 

15 

60^ 

75 

91 

106 

121 

136 

151 

166 

16 

72 

90 

108 

126 

144 

162 

180 

198 

17 

84^ 

105 

126 

148 

169 

190 

211 

235 

18 

98 

122 

147 

171 

196 

220 

245 

269 

19 

112H 

140 

169 

197 

225 

253 

280 

309 

20 

128 

160 

192 

224 

256 

288 

320 

352 

21 

144^ 

180 

217 

253 

289 

325 

361 

397 

22 

162 

202 

243 

283 

324 

364 

404 

445 

23 

179^ 

225 

271 

313 

359 

406 

452 

496 

24 

200 

250 

300 

350 

400 

450 

500 

550 

25 

220^ 

275 

331 

386 

441 

496 

551 

606 

26 

242 

302 

363 

423 

484 

544 

605 

666 

27 

265 

330 

397 

463 

530 

596 

661 

726 

28 

288 

360 

432 

504 

576 

648 

720 

792 

29 

312^ 

391 

469 

547 

625 

703 

782 

860 

30 

338 

422 

507 

591 

676 

761 

845 

930 

31 

364^ 

456 

547 

638 

729 

820 

912 

1004 

32 

392 

490 

588 

686 

784 

882 

980 

1078 

33 

421 

526 

631 

736 

842 

946 

1051 

1155 

34 

450 

562 

675 

787 

900 

1012 

1125 

1237 

35 

480^ 

601 

721 

841 

961 

1081 

1202 

1322 

36 

512 

640 

768 

896 

1024 

1152 

1280 

1408 

37 

544^ 

681 

817 

953 

1089 

1225 

1361 

1497 

38 

578 

723 

867 

1011 

1156 

1300 

1446 

1590 

39 

612^ 

765 

918 

1070 

1225 

1379 

1530 

1684 

40 

648 

810 

972 

1134 

1296 

1458 

1620 

1782 

41 

684^ 

850 

1027 

1198 

1369 

1541 

1711 

1882 

42 

721 

903 

1083 

1264 

1442 

1625 

1805 

1986 

43 

760^ 

952 

1141 

1331 

1521 

1711 

1902 

2091 

44 

800 

1000 

1200 

1400 

1600 

1800 

2000 

2200 

45 

840  1^ 

1051 

1261 

1471 

1681 

1891 

2102 

2312 

46 

882 

1103 

1323 

1544 

1764 

1985 

2206 

2426 

47 

9243/6 

1156 

1387 

1618 

1849 

2080 

2312 

2542 

48 

968 

1210 

1452 

1694 

1936 

2178 

2420 

2662 

49 

1012H 

1265 

1519 

1772 

2025 

2278 

2530 

2784 

50 

1058 

1322 

1587 

1850 

2116 

2380 

2645 

2909 

STRUCTURAL  DIAGRAMS   AND    TABLES 


237 


TABLE  46 

SPACING,  IN  INCHES,  OF  ROUND  BARS  FOR  REINFORCED  CONCRETE  PIPE  OR 
BANDS  FOR  WOOD  STAVE  PIPE  COMPUTED  FROM  THE  FORMULA 

A  9 

s  =  2.307  ™ '      S  =  10,000 
h  K 

(See  also  Fig.  41.) 


h  =  10 


h  =  15 


20 


h  =  25 


=  30 


6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
26 
28 


30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
54 
56 
58 
60 
62 
64 
66 
68 
70 
72 


6 


6 
6 

5K6 
4^6 
4  6 
3K6 


6 


2K5M 


1^6 


A 


6 

2K6 

2M5M 
4K 

1^4M 
3M 


IK 


4K 


4K6 


5^ 
5  4 

1M4M 

4K 

4K 

4  4 
4 

3% 

3K 
3K 


A 


3K 


3K6 


6 
6 

2^6 
2^6 
2K6 

2K 
2K 


5K 


4K 


4^6 
3K6 


IK 


4K 


5K 

5 

2K4K 


3K6 


2^6 
2M  6 
2K6 
2K 


2M 


IK 
IK 
IK 
IK 


M 


K  A 


4K 
4K 


3K 
3K 


1K3K 


2K 

2  4 


2^ 

2K 
2K 


IK 


6 
6 
6 
6 
6 

5K 

5 

4K 

4 

3K 
3M 


5K 


3 
2 
1 
IK 


6 

2M5M 


3K 
2K4K 


IK 

i_K 

M 


1K3^ 


3K 


1K3K 
IK 

3 
3 
3 


2^4K 
2K4 


2K5K6 
5M 


4K6 


1K3M6 
1K3K6 
1K3K6 
1K3M 


K 


This  table  is  based  on  a  stress  in  the  steel  of 
12,000  multiply  spacings  taken  from  table  by  1.2 
The  maximum  allowable  spacing  is  fixed  at  6 
diameter  of  the  steel. 

5    =  spacing  of  rods  or  bands,  in  inches. 
5    =  unit  stress  in  steel. 
A    =  cross-sectional  area  of  steel  rod  or  band, 
in  square  inches. 


10,000  #  per  square  inch.  For  a  unit  stress  of 
;  for  a  unit  stress  of  15,000  multiply  by  1.5,  etc. 
inches  and  the  minimum  at  1  inch  plus  the 


h  =  head  of  water  on  center  of  pipe  in  feet. 
R    =  inside  radius  of  pipe,  in  inches. 
/     =  diameter  of  steel  rod  or  band,  in  inches. 
D    =  inside  diameter  of  pipe,  in  inches. 


238 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


TABLE  46  (Continued) 


h  =  35 


h  =  40 


h  =  45 


6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
26 
28 


I* 


2 
15* 


6 
6 
6 

5K 


2M 


4 

3^ 

3 


6 
6 
6 
6 
6 

5y2 

4% 


13K 


6 
6 
5 

4 

I* 

23^ 


2 
15* 


3% 


H 


N 


1A 


30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
54 
56 
58 
60 
62 
64 
66 
68 
70 
72 


iy2 
i** 

IK 
IK 


4% 
4^ 
4M 


3K 
3K 
3 
3 


2 

2 
2 

2 


6 
6 
6 
6 

534 


4K 

4  4 
4 

35* 


15* 
15* 


K 


33^ 


6 
6 
6 
6 

53^ 


4 
4 

3M 
3M 


3% 


% 

3 


6 
6 

5% 


5 

434 


4 
4 

3  4 

3K 

3K 

3 

3 

3 


STRUCTURAL    DIAGRAMS    AND   TABLES 


239 


TABLE  46  (Continued) 


h  =  50 


h  =  60 


h  =  70 


K 


X 


K 


6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
26 
28 


2 

IK 


2% 

23^ 
2M 
2 

IK 

IK 


4 


33^ 


2 

IK 


6 

4M 
3M 
3 

2^ 

2M 
2 

IK 

1^ 

tH 

IK 


6 
6 

5M 
4% 
4 

33^ 
334 

2% 


6 
6 
6 
6 
6 

5M 
43^ 

4M 

334 

33^ 


IK 


4 

3M 


2 

IK 

1H 

IK 
IK 


6 
6 
5 

4 

3^ 
3 

2% 


IK 


30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
54 
56 
58 
60 
62 
64 
66 
68 
70 
72 


H 


iK 
IK 


2% 


2A 

2 

IK 

IK 

IK 


3 
3 
3 

2^ 
2M 


414 


3 
3 

2K 
2j| 


6 
6 
6 
6 
6 
5K 


4% 
4^1 


3/2 


2 

2 

15t 


3M 


4M 


2M 
2  2 
2 


IK 


5 

434 
4^ 

4  4 
4 

3K 

33^ 

3  2 


2K 


240 


,  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  46  (Concluded) 


80 


90 


100 


A 


X 


N 


M 


A 


M 


6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
26 
28 


4% 


3 

25* 

2  4 

2 

15* 

i>I 


3 

2^ 


15* 


2% 


15* 


2 

15* 

15* 


2 

2 

15* 

15* 


5* 


5* 


30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
54 
56 
58 
60 
62 
64 
66 
68 
70 
72 


2 
2 

15* 
15* 


2 
2 
2 

15* 
15* 


5% 


2% 


5M 


1J* 
1J* 

1M 


15* 


4 

4 
3% 


2 

2 
15* 

15* 
15* 
15* 


3 
3 

2% 
2% 


2M 

2  4 

2 

2 

2 

15* 


5 

4% 


3% 


For  rectangular  beams  c  =  —  and  / 


12 


and  the  formula 


becomes  5  = 


. 
0  a2 


The  values  of  c  and  I  for  other  shapes  of 


cross-section  may  be  found  in  any  standard  pocket-book. 

Table  43  is   convenient    for   proportioning   wooden   beams. 

b  d?         M 
This   table  gives  values  of  =  -=-,  where  M  is  in  foot- 

o  /\  LA         o 

pounds.     To  determine  the  size  of  a  rectangular  wooden  beam, 
divide  the  bending  moment  in  foot-pounds  (equal  to  the  bend- 


STRUCTURAL    DIAGRAMS   AND   TABLES  241 

ing  moment  in  inch-pounds  divided  by  12)  by  the  allowable 
stress  in  the  wood;  enter  the  diagram  with  the  resulting  quotient 
and  read  the  depth  and  width  of  beam  required.  Example:  A 
wooden  beam  is  to  be  subjected  to  a  bending  moment  of  50,000 
foot-pounds;  the  allowable  unit  stress  is  1,200  pounds 

per  square  inch;  -~-  =      '      •  =  41.7.    From  the  table  we  find 

o  1,ZUU 

that  a  12  x  16-inch    beam  gives  a  value  of  -~  of  42.67.  Other 

o 

combinations  of  b  and  d  also  approximate  the  desired  value  of 
MlS,  and  the  best  combination  to  use  must  be  decided  on 
economical  and  practical  considerations. 

Table  46  gives  the  spacing,  in  inches,  of  round  bars  for  pipes 
under  pressure.  It  is  intended  primarily  for  the  reinforcing 
bars  of  concrete  pipes,  but  may  also  be  used  for  determining  the 
spacing  of  bands  on  wood  pipe. 

Fig.  41  gives  similar  data,  but  covers  a  much  larger  range,  and 
is  especially  adapted  to  wood  stave  and  concrete  pipe  of  larger 
sizes  and  greater  heads  than  are  included  in  the  table.  This 
diagram  gives  without  computation  the  spacing  of  bands  or 
rods  for  heads  from  20  to  200  feet,  diameters  of  pipe  from  18  to 
120  inches,  diameters  of  steel  rods  or  bands  from  J^-inch  to 
1  inch,  and  stresses  in  steel  from  10,000  to  15,000  pounds  per 
square  inch. 

Example  of  Use  of  Diagram. — Given  a  60-inch  diameter  wood 
pipe  with  a  head  of  water  of  150  feet.  What  size  and  spacing  of 
bands  are  required,  the  working  stress  in  bands  to  be  12,000 
pounds  per  square  inch  ?  Solution :  Enter  the  diagram  at 
head  =  150  feet;  thence  horizontally  to  the  line  for  60-inch 
pipe;  thence  down  to  the  line  for  J^-inch  band.  Here  it  is 
noted  that  j^-inch  bands  would  require  a  spacing  of  0.57  inch. 
This  spacing  is  impracticable,  as  is  also  the  size  of  band  for 
this  pipe;  we,  therefore,  follow  diagonally  to  the  right  and 
note  that  J^-inch  bands  would  require  a  spacing  of  1  inch; 
continuing  down  diagonally  we  note  that  J^-inch  bands  would 
require  a  spacing  of  1.56  inches  and  %-inch  bands  would  re- 
quire a  spacing  of  2.25  inches.  If  it  is  decided  to  use  %-inch 
bands,  we  now  follow  down  vertically  to  the  line  for  10,000 


242 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


pounds  per  square  inch  stress;  thence  diagonally  to  the  right 
to  the  line  for  12,000  pounds  per  square  inch  stress  and  read 
the  spacing  2.7  inches  for  %-inch  bands,  for  a  60-inch  pipe 
under  a  head  of  150  feet,  the  working  stress  in  the  bands  being 
12,000  pounds  per  square  inch.  The  formula  on  which  the 
diagram  is  based  is  shown  on  the  drawing. 

Table  47  gives  miscellaneous  data  in  regard  to  the  design 
and  construction  of  wood  pipe. 

TABLE  47 

MISCELLANEOUS  DATA  FOR  WOOD  PIPE 
Economical  Thickness  of  Staves 


MACHINE-BANDED  PIPE 

CONTINUOUS  PIPE 

Diameter  of  Pipe, 

Thickness  of  Staves, 

Diameter  of  Pipe, 

Thickness  of  Staves, 

Inches 

Inches 

Inches 

Inches 

4 

1A 

24 

1^ 

6 

1A 

36 

*H 

8 

IK 

48 

1« 

10 

1H 

60 

l5/8or2ys 

12 

1  1% 

72 

2ys  or  2y2 

14 

1  1% 

84 

2y2  or  zy8 

16 

18 

IX 
1% 

96 
108 

25/8  or  3y8 

sy8  or  zy2 

20 

1* 

120 

35/8  or  4 

24 

1* 

132 

3%  or  4^ 

144 

3%  or  4^ 

MAXIMUM  CURVATURE  ON  WHICH  SOME  WOOD  STAVE  PIPES  HAVE  BEEN 

BUILT 


Diameter, 

Thickness 

Radius 

Radius  of  Curve 

Feet 

Inches. 

Feet 

Diameter  of  Pipe 

2.0 

IK 

58 

29 

2.5 
4.0 
4.7 
5.0 
7.0 

2 

89 

83 
100 
106 
296 

Horizontal 
Horizontal 
Vertical  Concave 
Vertical  Convex 
Horizontal 

35 
21 
21 
21 
43 

These  were  about  the  sharpest  curves  the  respective  pipes  would  stand. 

Convex  vertical  curves  (^^)  are  easiest  to  build;  concave  vertical  curves 
(  ^  )  are  next,  and  horizontal  curves  are  the  most  difficult  on  account  of 
the  difficulty  of  applying  the  necessary  pull  to  the  pipe  to  throw  it  into  the 
curve. 

NOTE. — The  above  data  on  thickness  of  staves  and  maximum  curvature  were  furnished 
by  Mr.  H.  D.  Coale.  Chief  .Engineer.  Pacific  Tank  and  Pipe  Company,  Portland,  Ore. 


STRUCTURAL   DIAGRAMS   AND   TABLES 


243 


s= Spacing,  center  to  center  of  rod  Cinches) 
0.20.250.3     0.4    0.50,60.70.80.91  1,5         2    2.5    3         4       5     6    7    8  9 10    12 


X  S      ^ 

"      1   ^\ 

^\ 

\      \  \ 

\ 

S 

5 

^ 

^  \  ^ 

S      V 

150 

\^ 

c 

v\\\  N  \  \ 

V 

s 

\ 

\ 

X  ^  .  \ 

\\\\  ^   \ 

\ 

\ 

\\ 

s. 

5i  ^     s.  N 

^    ^ 

~^s^Or' 

s  \ 

\ 

v 

\ 

^^   ^ 

\     ^^sX^\ 

\ 

\ 

\ 

^ 

\\\  \ 

\     v       > 

\   X^^s 

\ 

\ 

\ 

v    ^  \ 

\     \       \\v 

*  on  ... 

g90 

s-S    s  -N   - 

\s   <        jjSJ 

£  80  -  • 

^rN  •vN 

r^~  ^~^s 

\\    '  \ 

\ 

3  70 

.  *  \ 

\  ^ 

V 

!v  s  !  S 

^  ^      V  ^        ^ 

\         (        s  V 

\ 

\ 

>    ^ 

^s  N 

s.  \  S     .  ^ 

^L  \  \\ 

\ 

% 

\    V  A 

^-     s^    s 

vr^S 

X1 

s 

^\ 

\  \,   v 

V^^^i,^^^ 

i!!:  ]   S 

N\ 

\\ 

\ 

z 

S      v 

\>\^s,s  v  ^ 

\x 

V 

^ 

sX 

40    •  •  • 

\ 

•^       v\    ^S 

\       \   \ 

x\ 

\ 

X^\^¥S 

11L   '/  i^  Q^f  P 

g 

( 

\ 

r\C 

ffix\ 

flw 

^ 

\ 
i 

L 

ftp 

t 

20  tt<; 

dx 

\ 

\ 

\ 

\ 

\ 

\ 

\  \  v  v  s 

1! 

^;  "^ 

Jr  iJH  ^ 

XfXxX 

\ 

\ 

\ 

\ 

\ 
\ 

V\S\N^ 
\  \  ^  ^ 

s^v  x  \N 

•-  v  ^  s  ^  \ 

% 

\* 
1/2  1 

5/i 

%i 
1 

-8    1 

S 
ioooo-S| 
iiooo  g  5 

12  000  »S 
M  A 
13000.2" 

14000|§ 
15000  ^d 

(n 

i 

i 

i 

x 

\ 

X  ^    \x 

N  "  v  '   \ 

vs     >  \ 

\  \  \        s  sN 

S3 

^ 

I 

X 

\  ^      s^ 

\      \y  s  s 

v  X  S^  V^ 

V  ^  S  S         S 

\ 

4 

i 

\ 
*\ 

^\\ 

\\  \ 

\  \  S     s  \  ^ 

ill 

\ 

V 

; 

x     \  \  S 

\  s  \     \ 

s         \ 

X       V      \ 

Sx    S^ 

S  x  ^     \  \\  s 

x  \    sS  o 

^^ 

5    '    X        \ 

!||j| 

\    \    \  v  ss 

Sl^ 

1 

\ 
\^ 

\ 

\ 

\ 
\ 

^      ^ 

;  J  5  J     S 

ll 

111  V' 

11 

1 

X 
K 

\ 

x\ 

\ 

i 

\           \    S  \ 

xiv  \ 

^X  ^s  \  X 

^l|  Hi? 

:vl|^ 

1 

A 
\ 

X^ 

l 

\   \    \    ^ 
\^\   \    \   S 

io;^ 

Formula 
2-307  £f- 
spacing  in  inches 
area  of  band  or  rod  in  sq.ins. 
unit  stress  in  band  or  rod 
head  of  water  in  feet  on  centei 
of  pipe 
inside  radius  of  pipe  in  inches 

\ 

\\\^\\\ 

M$\ 

\ 

\ 

\ 

s\\\^ 

\A\  \ 

A 
\ 

\^^\^ 

All 

x 

\ 

\\^J 

'xV  r 

s 

s  j^ 

3-K  1 

1 

\ 

\ 

\^\ 

i.  vvS 

v^N  tv 

SM;S 

\ 

y        S  * 

^V  JA 

x 

5S  S  \  H\ 

Av  KvSi 

\ 

.\ 

Si  ^ 

^  0  \ 

1            1.5        2     2.5    3         4        5     6     7    8  910   1 
s  =  Spacing  center  to  center  of  rod  (inches) 

FIG.  41.— Spacing  of  Bands  on  Wood  Stave  Pipe  and  Reinforcement  Rods 

in  Concrete  Pipe. 


244  WORKING  DATA  FOR  IRRIGATION   ENGINEERS 

SIZE  OF  WIRE  USUALLY  USED  FOR  WINDING  MACHINE-BANDED  PIPE 


Gage 
Number 

Diameter, 
Inches 

Area, 
Square  Inches 

Breaking  Strength  at 
60,000  Lbs.  per  Sq.  In. 

0.  . 

.307 

.074 

4440 

1  

2  
4 

.283 

.263 
225 

.063 
.054 
040 

3774 
3258 

2388 

6. 

192 

029 

1734 

8  

.162 

.021 

1236 

Fig.  42  gives  the  thickness  of  steel  pipe  for  three  different 
efficiencies  of  joint,  single  riveted  at  55  per  cent,  best  double 
riveted  at  72  per  cent,  and  lock-bar  pipe  at  90  per  cent.  The 
lock-bar  joint  is  capable  of  developing  100  per  cent  efficiency;  but, 
due  to  occasional  defects  in  material  or  workmanship  on  the 
lock-bars,  an  efficiency  of  90  per  cent  is  recommended  for  cal- 
culating the  thickness.  The  thickness  given  in  the  diagram  is 
the  net  thickness  of  steel  required  to  withstand  the  given  pressure 
at  a  unit  stress  in  the  steel  of  16,000  pounds  per  square  inch.  It 
is  customary  to  allow  a  slight  excess  of  thickness  to  take  care  of 
the  weakening  by  corrosion. 

The  following  table  *  gives  the  greatest  allowable  depth  of 
earth  cover  over  steel  pipe  in  feet.  If  a  pipe  is  to  be  subjected 
to  a  greater  pressure  of  earth  than  indicated  in  the  table,  the 
thickness  must  be  increased  or  the  pipe  shell  reinforced  with 
angle  irons  or  other  suitable  shapes. 


DIAMETER  OF  PIPE 


Thickness 

30 
Inches 

36 
Inches 

42 
Inches 

48 
Inches 

54 
Inches 

60 
Inches 

72 
Inches 

8 

5 

8 

'5 

'i 

'3 

12 

9 

6 

5 

4 

3 

2 

3/ 

18 

12 

9 

7 

6 

4 

3 

_7_ 

25 

17 

12 

9 

8 

6 

4 

I/ 

22 

16 

12 

10 

8 

6 

5/8 

15 

12 

9 

*  Figures  taken  from  "American  Civil  Engineers'  Pocket  Book,"  Mansfield  Merriman,  Editor- 
in-Chief,  John  Wiley  &  Sons,  New  York  City. 


STRUCTURAL    DIAGRAMS   AND   TABLES 


245 


.2170  H^ormula 

it  =   thickness  of  shell  in  inches 
diameter  of  pipe    "       »» 
head  of  water 
unit  stress  in  steel  =  16  000 
c.  =  efficiency  of  joint 

Approximate  weight  per 

linear  foot: 

(12.5  x  diameter  x  thickness) 
+ 10  Ibs. 


Best  Double  Riveted  72-* 


:-bar  90%  efficiency  of  joint 


Thickne&b  In  Inches   (working  Strees  16  000  #/n"j 


FIG.  42.— Thickness  and  Weight  of  Steel  Pipe. 


246  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

Example  oj  Use  of  Diagram. — Given  a  72-inch  steel  pipe  for 
a  power  plant  under  a  static  head  of  200  feet;  an  allowance  of 
50  per  cent  is  to  be  made  for  water-ram  and  10  per  cent  for  cor- 
rosion, making  the  total  head  (200  X  1.60)  =  320  feet.  Enter 
the  diagram  at  a  head  of  320  feet,  thence  horizontally  to  the  line 
for  72-inch  pipe,  then  vertically  down  and  read  thickness  slightly 
more  than  /{6  inch  for  single-riveted  joint,  slightly  less  than 
J{6  inch  for  double-riveted  joint,  and  slightly  more  than  1%2  inch 
for  the  lock-bar.  Single  riveting  is  seldom  used  for  any  but 
unimportant  and  temporary  structures.  Carrying  the  above 
example  further,  we  note  from  the  foregoing  table  that  the 
/16-inch  shell  will  withstand  a  back-fill  of  4  feet,  and  the  "^-indi 
shell  will  withstand  between  2  and  3  feet.  The  approximate 
weight  of  the  pipe  is  given  by  the  formula  shown  in  the  diagram. 
Table  48  gives  the  American  Water  Works  Association 
Standards  for  thickness  and  weight  of  cast-iron  pipe. 

Table  49  gives  the  dimensions  and  weights  of  metal  flumes 
as  manufactured  by  the  Hess  Flume  Co.  of  Denver,  Col. 

Fig.  43  gives  the  pressure  of  water  in  pounds  per  square  inch, 

corresponding  to  heads  up  to  460  feet.    The  diagram  contains 

two  pairs  of  scales,  those  at  top  and  left  belonging  to  the  upper 

line,  and  those  at  bottom  and  right  belonging  to  the  lower  line. 

Example  1- — What  is  the  pressure  corresponding  to  a  head  of 

97  feet?    Enter  the  diagram  on  the  left  at  a  head  of  97  feet, 

thence  horizontally  to  the  upper  line,  thence  vertically  to 

the  top  scale  and  read  42  pounds  per  square  inch. 

Example  2. — What  is  the  pressure  corresponding  to  a  head  of 

285  feet?    Enter  the  diagram  on  the  right  at  a  head  of  285 

feet,  thence  horizontally  to  the  lower  line,  thence  vertically  to 

the  lower  scale  and  read  124  pounds  per  square  inch. 

Fig.  44  gives  the  pressure  of  water  in  pounds  per  square  foot 

for  heads  up  to  380  feet.    Its  construction  and  manner  of  use  are 

similar  to  Fig.  33. 

Fig.  45  gives  the  total  horizontal  hydraulic  pressure  on  a  wall 
1  foot  long  for  heads  up  to  100  feet.  This  diagram  is  useful  in 
the  design  of  dams  and  retaining  walls.  For  retaining  walls  for 
resisting  earth  pressures  without  surcharge,  the  pressures  given 
by  the  diagram  may  be  multiplied  by  0.35  to  0.45  according  to 


STRUCTURAL  DIAGRAMS  AND   TABLES 


247 


the  nature  of  the  back-filling  material,  to  obtain  the  total  earth 
pressure.  For  pressures  up  to  30  feet,  the  lower  line  and  lower 
scale  are  used.  For  pressures  from  30  to  100  feet,  the  upper 
line  and  upper  seals  are  used. 

Example  1- — What  is  the  total  pressure  on  section  of  wall  10  feet 
long  under  a  hydrostatic  head  of  75  feet?  Enter  the  diagram 
on  the  left  at  a  head  of  75  feet,  thence  horizontally  to  the 
upper  line,  thence  vertically  to  the  upper  scale,  and  read 
176,000  pounds  for  a  section  of  wall  1  foot  long.  For  the 
10-foot  section  the  pressure  will,  therefore,  be  1,760,000 
pounds. 

Example  2. — A  retaining  wall  for  earth  is  25  feet  high.  What  is 
the  total  earth  pressure  on  a  section  of  the  wall  8  feet  long? 
From  the  lower  line  of  the  diagram  we  read  the  hydro- 
static pressure  to  be  19,500  pounds  per  linear  foot  of  wall. 

TABLE  48 

CAST-IRON  PIPE — THICKNESS  AND  WEIGHT 
(American  Water  Works  Association  Standards) 


CLASS  A 

CLASS  B 

100  FEET  HEAD 

200  FEET  HEAD 

43  POUNDS  PRESSURE 

86  POUNDS  PRESSURE 

Nomi- 

nal 

Inside 

Weight  per 

Weight  per 

Diam- 
eter 

Thick- 

Thick- 
ness, 

Inches 

ness, 
Inches 

Foot 

12-Foot 
Length 

Inches 

Foot 

12-Foot 
Length 

Laid 

Laid 

4 

.42 

20.0 

240 

.45 

21  7 

260 

6 

.44 

30.8 

370 

.48 

33.3 

400 

8 

.46 

42.9 

515 

.51 

47.5 

570 

10 

.50 

57.1 

685 

.57 

63.8 

765 

12 

.54 

72.5 

870 

.62 

82.1 

985 

14 

.57 

89.6 

1075 

.66 

102.5 

1230 

16 

.60 

108.3 

1300 

.70 

125.0 

1500 

18 

.64 

129.2 

1550 

.75 

150.0 

1800 

20 

.67 

150.0 

1800 

.80 

175.0 

2100 

24 

.76 

204.2 

2450 

.89 

233.3 

2800 

30 

.88 

291.7 

3500 

1.03 

333.3 

4000 

36 

.99 

391.7 

4700 

1.15 

454.2 

5450 

42 

1.10 

512.5 

6150 

1.28 

591.7 

7100 

48 

1.26 

666.7 

8000 

1.42 

750.0 

9000 

54 

1.35 

800.0 

9600 

1.55 

933.3 

11200 

60 

1.39 

916.7 

11000 

1.67 

1104.2 

13250 

72 

1.62 

1283.4 

15400 

1.95 

1545.8 

18550 

84 

1.72 

1633  .  4 

19600 

2.22 

2104.2 

25250 

All  weights  include  standard  sockets. 


248 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  48  (Concluded) 
CAST-IRON  PIPE — THICKNESS  AND  WEIGHT 


CLASS  C 

CLASS  D 

300  FEET  HEAD 

400  FEET  HEAD 

130  POUNDS  PRESSURE 

173  POUNDS  PRESSURE 

Nomi- 
nal 

Weight  per 

Weight  per 

Inside 

1*U  I«tw 

Thick- 

Diame- 

1  niclc- 

ness, 

eter, 
Inches 

ness, 
Inches 

Foot 

12-Foot 

Length 

Inches 

Foot 

12-Foot 
Length 

Laid 

Laid 

4 

.48 

23.3 

280 

.52 

25.0 

300 

6 

.51 

35.8 

430 

.55 

38.3 

460 

8 

.56 

52.1 

625 

.60 

55.8 

670 

10 

.62 

70.8 

850 

.68 

76.7 

920 

12 

.68 

91.7 

1100 

.75 

100.0 

1200 

14 

.74 

116.7 

1400 

.82 

129.2 

1550 

16 

.80 

143.8 

1725 

.89 

158.3 

1900 

18 

.87 

175.0 

2100 

.96 

191.7 

2300 

20 

.92 

208.3 

2500 

1.03 

229.2 

2750 

24 

1.04 

279.2 

3350 

1.16 

306.7 

3680 

30 

.20 

400.0 

4800 

1.37 

450.0 

5400 

36 

.36 

545.8 

6550 

1.58 

625.0 

7500 

42 

.54 

716.7 

8600 

1.78 

825.0 

9900 

48 

.71 

908.3 

10900 

1.96 

1050.0 

12600 

54 

1.90 

1141.7 

13700 

2.23 

1341.7 

16100 

60 

2.00 

1341.7 

16100 

2.38 

1583.3 

19000 

72 

2.39 

1904.2 

22850 

84 



All  weights  include  standard  sockets. 

The  total  hydrostatic  pressure  on  an  8-foot  section,  there- 
fore, is  19,500  X  8  =  156,000  pounds.  The  earth  pressure 
will  equal  from  0.35  to  0.45  of  this,  or  55,000  to  70,000  pounds, 
depending  upon  the  nature  of  the  back-fill,  the  material 
having  the  steepest  angle  of  repose  producing  the  smallest 
pressure,  and  vice  versa. 

Fig.  46  gives  the  theoretical  horse-power  of  falling  water. 
The  diagram  gives  horse-powers  directly  for  quantities  up  to 
75  c.  f .  s.  and  falls  up  to  50  feet.    The  diagram  may  be  used  for 
higher  values  of  quantity  or  fall  by  dividing  by  10  before  enter- 
ing the  diagram,  and  then  multiplying  the  resulting  power  by  10. 
Example  1. — What  horse-power  is  produced  by  45  c.f.s.  of  water 
falling  27  feet?     Enter  the  diagram  at  the  lower  scale  at 
Q  =  45,  thence  vertically  to  the  line  representing  a  fall  of 
27  feet,  thence  horizontally  to  the  scale  at  the  left  and  read 
138  horse-power. 


STRUCTURAL  DIAGRAMS   AND   TABLES 


249 


3-3  B   I 

.SP5^ 

£^o 
£"30 


O 


OSC^^OS 


ssssss 


i— i<NCOCO"**O<OI>OOOOC5OO'— i 


(N(N(N(N<N<N(N(N(N(N(N(N(N<N 


<N  <M  (M 


^V'SS-g 
TO0     32 

S     ^^ 


\w\oo\oo\oo\oo 

CO\CO\CO\C»S\eO\ 

T^yH-rJ<T^rtl^TtlTtHT^^TtlTjHCOCOCOCO 

co  co  co  co  co  co  co  co  co  co  co  co  co  co  co  co 


C^ 

to 


lococo  coco  cococococo  coco  co  coco  cocor-ir-i^-iTH^H 


QOOOCOI>-i—  I 


OOi—  I  TH  i—  (»-iC<l(MCOCO-^l>OiOCOI>l>QOOOO5OOi—  i 


^^ 

H2! 


?3<N  (N  C^< 


250 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


Pressure  of  Water 

(pounds  per  sq.  inch) 
p  =  Pressure  in  pounds  per  square  inch 


lOOf-rrn 

5              10             15 

20             25 

30 

35            40 

45            50^^ 

ead  of  water  in  feet 

£§gg82£!gg?g8 

Pressure  of  Water  i 
Corresponding  t 
Calculated  frc 

Q  Pounds  per  sq.  i 
o  Different  Heads 
>m  the  Formula 
434H 

--at  " 

IK 
\ 

h 

i 

!/ 

^EEEEE 

lilllliilll 

lead  of  water  in  feet 

K     ::: 

II  40--- 
I      

35  
30  
25  
20  
15  
10  

oLLL 

.  -220 
200 

140 

120 

40  60  80  100  120          140 

p  =  Pressure  in  pounds  per  square  inch 

FIG.  43. 


160 


180 


200 


STRUCTURAL   DIAGRAMS   AND   TABLES 


251 


100°mTf 

p=  Pressure  in  Pound 

00        1000       1500       2000      2500       3000      350C 

Pressure  of  Water 

18  per  Sq.Foot  (Pounds  per  Sq.  Foot) 
4000      4500       5000       5500      6000 

75  



45  :  :  :  : 

-  :  Pressure  of  Water  in  Pounds  per  Squ 
Corresponding  to  Different  He 
Calculated  from  Formula 

[[     Lfffl 

are  Foot      :            :            7 
ads             -----------  f--- 

1  i  1  i  1  i  1  -ft---              --400 
--2---                  ---^380 
2t  4  360 
^  .2  340 
_^  -t  320 
2t  300 
2t..     280  fr 

35  
30  

20  -- 
15  
10  
5  --7* 
gEE 

efe  L. 

m    III  ill 

4000      6000       8000      10000    12000  1400 
jp  =  Pressure  in  Pound 

^z::!::::::::::::::::240^ 

1  IN  1  1  1  1|  ||  1  1  1|  1  1  HI  [    w 

:__::     :::::::::     :       x 

160 

---  -  140 
120 

--100 

:::::::  so 

0     16000    18000    20000    22000    24000 
3  per  Sq.Foot 

FIG.  44. 


252 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


Total 
Hydrostatic  Pressure 

p  =  Total  Hydrostatic  Pressure  in  Thousands  of  Pounds 


r 

345 


30 


25 


20 


50 


100 


150 


250 


300 


I      I      I      I      I      I      I      I      I      I      I' 


Total  Hydrostatic  Pressure  on  Walls  and  Dams 
Calculated  from  the  Formula 
H2 


W*  weight  of  a  cubic  foot  of  water 
H  -  height  of  wall  or  dam 
p  =  total  pressure  per  linear  foot 
Note  :-For  retaining  walls  for  earth 
without  surcharge  multiply  the 
values  taken  from  this  diagram 
by  0.35  to  0.45 


0  5  10  15  20 

p  =  Total  Hydrostatic  Pressure  in  Thousands  of  Pounds 

FIG.  45. 


30 


STRUCTURAL  DIAGRAMS   AND   TABLES 


253 


400 


Horse  Power 

50 


45 


40 


35 


350 


250 


5150 


•100 


Theoretical  Horse  Power  of  Falling  Water 
Calculated  from  Formula: 

HQ 


i  n  — . 


8.81 


Q  =  Discharge  in  Cubic  Feet  per  Second 
H  =  Fall  of  Water  in  Feet 


25' 


15 


10 


0         5        10        15        20       25        30        35       40        45        50        55 

Quantity  c.f  .s.=  Q 
FIG.  46. 


70       75 


254  WORKING  DATA  -FOR  IRRIGATION   ENGINEERS 

Example  2. — What  horse-power  is  produced  by  155  c.f.  s.  dropping 
30  feet?  155  c.  f.  s.  is  not  represented  on  the  diagram,  but 
15.5  c.f.s.  is.  We,  therefore,  enter  at  15.5  c.f.s.,  and  following 
through  the  same  process  as  in  example  1,  read  52  horse- 
power. This  is  only  one-tenth  of  the  real  horse-power,  as  the 
quantity  used  was  only  one-tenth  of  the  real  quantity.  The 
real  horse-power  is,  therefore,  520. 

Example  3. — What  horse-power  is  produced  by  65  c.  f .  s.  dropping 
120  feet?  120  feet  fall  is  not  represented  on  the  diagram,  but 
12  feet  is.  We,  therefore,  enter  the  diagram  at  Q  =  65,  and 
from  the  line  representing  a  fall  of  12  feet,  read  89  horse- 
power. The  real  horse-power  is,  therefore,  890. 

Example  4. — What  horse-power  is  produced  by  160  c.f.s.  dropping 
230  feet?  In  this  case,  both  quantity  and  fall  must  be 
divided  by  10  before  entering  the  diagram,  and  the  horse- 
power read  must  then  be  multiplied  by  100.  Entering  the 
diagram  with  Q  =  16  and  H  =  23  we  read  the  horse-power 
to  be  47.  The  real  horse-power,  therefore,  is  4,700. 


CHAPTER  VI 

MISCELLANEOUS  TABLES 
AND . DATA 


CHAPTER  VI 
MISCELLANEOUS   TABLES  AND   DATA 

TABLE  50 
AVERAGE  WEIGHT,  IN  POUNDS  PER  CUBIC  FOOT,  OF  VARIOUS  SUBSTANCES 


Substance 


Weight 


Substance 


Weight 


Clay,  earth  and  mud : 

Clay 

Earth,  dry  and  loose .  .  . 

Earth,  dry  and  shaken . 

Earth,  dry  and  moderately 
rammed 

Earth,  slightly  moist,  loose 

Earth,  more  moist,  loose . . 

Earth,  more  moist,  shaken 

Earth,  more  moist,  moder- 
ately rammed 

Earth,  as  soft  flowing  mud 

Earth,  as  soft  mud  well 
pressed  into  a  box .  .  . 

Mud,  dry,  close 

Mud,  wet,  moderately 
pressed 

Mud,  wet,  fluid 

Masonry  and  its  materials: 

Brick,  best  pressed 

Brick,  common  hard.  .  .  . 

Brick,  soft,  inferior 

Brickwork,  pressed  brick, 

fine  joints 

Brickwork,medium  quality 
Brickwork,  coarse,  inferior 

soft  bricks 

Cement,  pulverized,  loose . 

Cement,  pressed 

Cement,  set 

Concrete,  1:3:6 

Gravel,  loose 

Gravel,  rammed 

Masonry     of    granite     or 
stone  of  like  weight: 

Well  dressed 

Well-scabbled      rubble, 

20  per  cent  mortar. 
Roughly    scabbled 
rubble,  25  per  cent  to 
35  per  cent  mortar. 
Well-scabbled   dry 
rubble. . 


122-162 

72-80 
82-92 

90-100 
70-76 
66-68 
75-90 

90-100 
104-112 

110-120 
80-110 

110-130 
104-120 


150 
125 
100 

140 
125 

100 
72-105 

115 
168-187 

140 

82-125 
90-145 


165 
154 

150 

138 


Masonry  and  its  materials 
(continued) : 

Roughly-scabbled      dry 

rubble 

Masonry  of  sandstone  or 
stone"  of  like  weight 
weighs  about  seven- 
eighths  of  the  above. 

Mortar,  hardened 

Sand,  pure  quartz,  dry, 
loose 

Sand,  pure  quartz,  dry, 
slightly  shaken.. .  . 

Sand,  pure  quartz,  dry, 
rammed 

Sand,  natural,  dry,  loose 

Sand,       natural,      dry, 
shaken 

Sand,  wet,  voids  full  of 
water 

Stone 

Stone,  quarried,  loosely 
piled 

Stone,  broken,  loose 

Stone,  broken,  rammed. 

Metals  and  alloys 

Brass  (copper  and  zinc) .  . 
Bronze  (copper  and  tin) .  . 

Copper,  cast 

Copper,  rolled 

Iron  and  steel,  cast 

Average 

Iron  and  steel,  wrought.  . 

Average 

Spelter  or  zinc 

Tin,  cast 

Steel 

Tin 

Zinc 

Mercury  (32°  F.) 

Woods: 

See  page  233 


125 

90-115 
87-106 
92-110 

100-120 
80-110 

85-125 

118-128 
135-195 

80-110 
77-112 
79-121 


487-524 
524-537 
537-548 
548-562 
438-483 

450 
475-494 

480 

425-450 
450-470 

490 

459 

438 

849 


257 


258  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

TABLE  51 
CONVENIENT  EQUIVALENTS 

LENGTH 

(See  Table  53) 

SURFACE 

1  square  inch  =  .006944  square  foot  =  .0007716  square  yard  =  .0000001594 

acre  =  .0000000002491  square  mile  =  6.45163  square  centimeters. 
1  square  foot  =  144  square   inches  =  £    square  yard  =  .000022957  acre  = 

.00000003587  square  mile  =  .092903  square  meters. 
1   square   yard  =  1,296   square   inches  =  9   square   feet  =  .0002066  acre  = 

.0000003228  square  mile  =  .83613  square  meter. 
1  acre  =  6,272,640  square  inches  =  43,560  square  feet  =  4,840  square  yards 

=  .0015625  square  mile  =  208.71  feet  square  =  .404687  hectare. 
1    square    mile  =  4,014,489,600    square   inches  =  27,878,400   square   feet  = 

3,097,600  square  yards  =  640  acres  =  259  hectares. 
1  square  meter  =  10,000  square  centimeters  =  .0001  hectare  =  .000001  square 

kilometer  =  1,550  square  inches  =  10.7639  square  feet  =  1.19598  square 
002471  acre  =  .0000003861  square  mile. 


, 
yards  =  .0002471  acre 


VOLUME 


1  cubic  inch  =  .004329  U.  S.  gallon  =  .0005787  cubic  foot  =  16.3872  cubic 

centimeters. 
1   U.  S.  gallon  =  231  cubic  inches  =  .13368  cubic  foot  =  .00000307  acre- 

foot  =  3.78543  liters. 
1  cubic  foot  =  1,728  cubic  inches  =  7.4805  U.  S.  gallons  =  .037037  cubic 

yard  =  .000022957  acre-foot  =  28.317  liters. 
1  cubic  yard  =  46,656  cubic  inches  =  27  cubic  feet  =  .00061983  acre-foot  = 

.76456  cubic  meter. 
1  acre-foot  =  325,851  U.  S.  gallons  =  43,560  cubic  feet  =  1,613^  cubic  yards 

=  1,233.49  cubic  meters. 
1  cubic  meter,  stere  or  kiloliter  =  1,000,000  cubic  centimeters  =  1,000  liters 

=  61,023.4  cubic  inches  =  264.17  U.  S.  gallons  =  35.3145  cubic  feet  = 

1.30794  cubic  yards  =  .000810708  acre-foot. 

HYDRAULICS 

1  U.  S.  gallon  of  water  weighs  8.34  pounds  avoirdupois. 

1  cubic  foot  of  water  weighs  62.4  pounds  avoirdupois. 

1  second-foot  =  448.8  U.  S.  gallons  per  minute  =  26,929.9  U.  S.  gallons  per 

hour  =  646,317  U.  S.  gallons  per  day. 
=  60  cubic  feet   per   minute  =  3,600  cubic   feet   per   hour  = 

86,400  cubic  feet   per  day  =  31,536,000  cubic  feet  per 

year  =  .000214  cubic  miles  per  year. 
=  .9917    acre-inch    per    hour  =  1.9835    acre-feet    per    day  = 

723.9669  acre-feet  per  year. 
=  50  miner's  inches  in  Idaho,  Kansas,  Nebraska,  New  Mexico, 

North   Dakota,  and  South  Dakota  =  40  miner's  inches 

in    Arizona,    California,    Montana,    and    Oregon  =  38.4 

miner's  inches  in  Colorado. 
=  .028317  cubic  meters  per  second  =  1.699  cubic  meters  per 

minute  =  101.941  cubic  meters  per  hour  =  2,446.58  cubic 

meters  per  day. 


MISCELLANEOUS   TABLES   AND   DATA 


259 


1   cubic   meter  per   minute  =  .5886   second-feet  =  4.403   U.   S.   gallons  per 

second  =  1.1674  acre-feet  per  day. 
1    million   gallons  per  day  =  1.55   second-feet  =  3.07  acre-feet   per   day  = 

2.629  cubic  meters  per  minute. 
1  second-foot  falling  8.81  feet  =  1  horse-power. 
1  second-foot  falling  10  feet  =  1.135  horse-power. 
1  second-foot  falling  11  feet  =  1  horse-power,  80  per  cent  efficiency. 
1  second-foot  for  1  year  will  cover  1  square  mile  1.131  feet  or  13.572  inches 

deep. 
1  inch  deep  on  1  square  mile  =  2,323,200  cubic  feet  =  .0737  second-feet  for 

1  year. 

MISCELLANEOUS 

1  foot  per  second  =  .68  mile  per  hour  =  1.097  kilometers  per  hour. 
1  avoirdupois  pound  =  7,000  grains  =  .4536  kilogram. 

1   kilogram  =  1,000  grams  =  .001   tonne  =  15,432  grains  =  2.2046   pounds 
avoirdupois. 

{15  pounds  per  square  inch. 
1  ton  per  square  foot. 
1  kilogram  per  square  centimeter. 

Acceleration  of  gravity,  g,  =  32.16  feet  per  second  per  second. 
1  horse-power  =  5,694,120  foot-gallons  per  day  =  550  foot-pounds  per  second 
=  33,000  foot-pounds  per  minute  =  1,980,000  foot-pounds  per  hour  = 
76  kilogrammeters  per  second  =  1.27  kilogrammeters  per  minute  =  746 
watts. 


TABLE  52 
INCHES  AND  FRACTIONS  EXPRESSED  IN  DECIMALS  OF  A  FOOT 


Inches 


FRACTIONS  OF  INCHES 


0 

H 

M 

H 

H 

5/s 

H 

ys 

0 

.0000 

.0104 

.0208 

.0313 

.0417 

.0521 

.0625 

!0729 

1 

.0833 

.0937 

.1041 

.1146 

.1250 

.1354 

.1458 

.1562 

2 

.1667 

.1771 

.1875 

.1980 

.2084 

.2188 

.2292 

.2396 

3 

.2500 

.2604 

.2708 

.2813 

.2917 

.3021 

.3125 

.3229 

4 

.3333 

.3437 

.3541 

.3646 

.3750 

.3854 

.3958 

.4062 

5 

.4167 

.4271 

.4375 

.4480 

.4584 

.4688 

.4792 

.4896 

6 

.5000 

.5104 

.5208 

.5313 

.5417 

.5521 

.5625 

.5729 

7 

.5833 

.5937 

.6041 

.6146 

.6250 

.6354 

.6458 

.6562 

8 

.6667 

.6771 

.6875 

.6980 

.7084 

.7188 

.7292 

.7396 

9 

.7500 

.7604 

.7708 

.7813 

.7919 

.8021 

.8125 

.8229 

10 

.8333 

.8437 

.8541 

.8646 

.8750 

.8854 

.8958 

.9062 

11 

.9167 

.9271 

.9375 

.9480 

.9584 

.9688 

.9792 

.9896 

12 

1.0000 

260 


8 


-IS! 


- 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 

I 


,34 


s 


I 


§! 


MISCELLANEOUS   TABLES   AND   DATA  261 


Table  57  is  designed  for  use  in  stadia  work  and  gives 
the  difference  in  elevation  corresponding  to  specified  slant 
distances  for  vertical  angles  of  0°  to  20°.  The  horizontal  dis- 
tances corresponding  to  the  slant  distances  are  also  given  for 
various  vertical  angles. 

Example. — With  the  instrument  at  A  a  vertical  angle  of 
3°  10'  is  observed  on  a  point  B  which  is  distant  350  feet  by 
stadia  reading;  find  the  difference  in  elevation  of  A  and  B  and 
the  horizontal  distance  A  B.  Opposite  3°  10'  in  the  first  column 
of  the  table,  16.5  is  found  under  a  distance  of  300  and  22.1  under 
a  distance  of  400;  and  interpolation  for  a  distance  of  350  feet 
gives  19.3  feet  for  the  difference  in  elevation  of  A  and  B.  Inter- 
polation for  350  between  the  values  in  the  300  and  the  400  dis- 
tance columns  of  the  horizontal  distance  lines  at  3°  and  4°  gives, 
respectively,  349.0  and  348.2;  and  an  additional  interpolation 
gives,  for  an  angle  of  3°  10'  and  a  slant  distance  of  350,  a  hori- 
zontal distance  of  348.9.  The  horizontal  distance  of  A  B  is, 
therefore,  348.9  feet. 

Another  method  of  making  interpolations  is  as  follows: 
Opposite  3°  10'  read  as  before,  16.5  feet  vertical  distance  under 
the  slant  distance  300;  then  under  the  slant  distance  500  and 
vertical  angle  3°  10'  read  27.6  feet, — and  divide  this  by  10  to  get 
the  vertical  distance  for  50  feet  equals  2.76;  add  this  to  16.5  and 
obtain  19.3  as  the  vertical  distance  for  350  feet.  By  a  similar 
process  the  horizontal  distances  are  found.  If  the  slant  dis- 
tance were  355  feet  the  vertical  distance  would  be  16.5  + 
27.6  ,  27.6 

~To~     Too" =  19'5' anc* so  on* 


262 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  54 

TABLE  FOR  CONVERTING  METERS  AND 


METERS  CONVERTED  INTO  FEET 


METERS 

O 

10 

20 

30 

4O 

5O 

6O 

7O 

8O 

9O 

1OO 

11O 

12O 

130 

14O 

ISO 

160 

17O 

ISO 

19O 

2OO 

21O 

220 

230 

24O 

250 

26O 

27O 

28O 

29O 

30O 


.8083 


I3I-2"', 
164 


.233 
Ov2 
041 


.6581 
4664 

-319/64 

.2747 


295 

328  .083 


.8913 

'/32 

7000 


QQQ-813 

030  .70( 

426 :Bn 

45g-3",. 


492:124-5 

524:^8 


.7411 


•  5494 

-4'%4 

.3577 

666-.iar 
688  -$& 

70l-925/64 

/2I  .7826 

764:iJSi 

787:^2 

820  .2083 

863:8;?- 
886:83- 


9511;% 


3-3a/s 
.2801 

36:j;'" 
68: 


2808 
1Vi« 
0891 


|Q/-611/64 

I04 


74 
05/37 

J1Vo4 

.5140 


107   .3223 

200:lSif. 

non-ir7^ 

202  .9389 

265 
298 
33l:43M' 


.7472 

•643/64 

.5555 


.1721 
QQC-1149/«* 
03  b  .9808 
/OO-916/3S 
423  .7887 


.4053 
~2136 
~02169 

-931/32 

.8302 

-721/32 
•62385 

T4468 

-3V,6 
.2551 

~049/64 

.0634 


•70  r 

720 


.8717 


000-555/64 

020   .4883 
QCC-39/i6 

000  .2966 


.1049 
.9132 

954  :f 215 

OO"I  ~  623/6^ 
307    .5298 


6-647/S4 
.5616 

39  .3700 
72  .1782 

in/. -ii"/32 

104  .9865 
IO7-917/32 

lO/  .7948 

1 70  .603? 


236:i4iU? 


.0280 

30I-.K 


400 


.6446 
-57/i« 
.4529 

-3V64 

.2616 

.0699 
/CC-10r/32 
4bO  .8778 
/QQ-815/64 
430  .6861 


.ino 
TftS 

~7276 
T5359 
T3442 

7  61  "j  525 
Tno-H17/32 

/JO  .9608 

"769*1* 
".5774 


OCO-0 
300 


.0023 
•  81064 


3 
9   . 

42  .6508 
7C  -51/2 
/O  .4591 

I08T26% 

|/|-029/32 

141  .0756 

|7Q-1039/64 

I/O  .8839 


-107/64 

.8424 


1922 
239*5006 
272~3088 

305:i','7i 
337 :1S? 


469 


COQ 
bOO 


.3918 

-213/32 

.2002 


.0085 
CQQ-95V64 

D30  .8168 


764'5 


QQfl 

OOU 


•4i34 

.2417 

-019/32 

.0499 
~85873 


895 


.6666 

QftQ_543/64 

320  .47249 
~28324 

994:J9/.'i 


4 

n^\" 


.12333 

-87/, 


.16448 

~iVSi 

~78H 
.5897 

~3980 
.2063 

Q7  /    -011/64 

0/4   .0146 


.4395 
.2478 
~.056T 

~67267 
CQC-549/64 
bOb  .4^10 

66972893 


7Q/ 
704 


.0976 

-107/8 

.9059 
.7142 

~  522*5 
OQQ-331/32 
000  .3308 


.1391 

-113/8 

.9474 


Ol   .7557 

964-.5667o 

nOTP-415/32 

337    .3723 


5-4-V 

I6.4043!2 

49:22;^ 
82 ov 


.0207 


14711% 


OlO-33^4 

2I0.2539 


.8705 

Ql|-89/64 

011.6788 

Q  /  /    5"/32 

044.4871 


.2954 


.7203 

50813: 

541:^9 
674:UM 

.9535 
.76J68 
"570*1 

".37844 
7OO-215/64 
700.1867 


.9950 
.8033 

-711/32 

.6116 

-51/32 

.4199 

-247/64 

.2282 
.0365 


836 
869 
902 


.8448 


NOTE:  Values  of  converted  even  meters  are  expressed 
of  1  foot.  For  example  74  meters  =  242 '-9 8/8"or  242.781'. 
table.  For  example  .3  meter  =  11.811  inches  =  .984  ft.= 
To  convert  147.678  meters  into  feet:147. 000  m= 482.282  ft, 

.6  «=  1.986" 
.07  "=  .229  " 
.008"=  .026" 


From  Engineering  News.March  12, 1914, 

Reproduced  by  permission  of  the  originator,  Mr.  H. P. Quick, 

Consulting  Engineer,  New  York. 


147.G78m=484.505 


MISCELLANEOUS   TABLES   AND   DATA 


263 


TABLE  54  (Concluded') 

MILLIMETERS  INTO  FEET  AND  INCHES 


WITH  INCHES  TO  NEAREST  64™      IOTHS  ETC.  OF  i  METER  CONVERTED  mo 


®B'* 
19  .6849 

52S 
851o16 


.1098 


18313? 


2161347 
2491& 

282:i5(36 


3861% 

413-1819 


.0011 


544ir 


p/,n-033/64 
040.0426 


.2343 

O33/* 


.8509 
"65922 

-3Vn 


774:3$ 


839  : 


.7008 


938:^' 
003:9P' 


7 

10-1119/Sa 

22.9658 
55"779414 


-663/s 
.5824 


I54:?; 


IO/  .0073 

0|Q-925/32 

219.8194 

orn-731/64 
252.6231 


31813s 

351:8481 


4I61& 


-  3^/64 

.2820 


547:l§t 


646:1215 


.7484 


.17^33 
79816 
.  7899 


007:iSif 


8 

25-2^4 


.2466 
-021/3 


59:83fe 

I24:i! 
I57:5>A 


427998 

288T 


288T71/30 


nno 
2.16 


3871% 


485:88. 


CIC-935/6* 
DID  .7960 


682irfe 


2209 

748:§29t 


879  .2 


G2A 


97711 


9 

291$ 

62:433t7 

QC-147/64 

90.1440 

|Q7-ii27/64 

127  .9523 


METERS 


.3772 


.1855 
1OI-1159/6< 
2al  .9938 


.8021 
QC7-721/64 
007  .6104 

390:857 

423:i2?; 


.0357 


488:18°43e 
521  :Eft 
5541™1? 
587:37/" 


2685 


.0768 
.8851 

CQr-821/64 

050  .6934 

7l8-.IoT7 

75i-j;a 


84913% 


.5433 


8l5-£fe 

948S 
980:^82 


O 

1O 

20 

30 

40 

50 

60 

7O 

80 

90 
10O 
110 
120 
130.03 
140 
150 
16O 
170 


A 

INCHES 


3.937 
7.874 
11.811 
15.748 
19.685 
23.622 
27.559 
31.496 
35.433 


.04 
,05 
06 


.07 

180.08 


190 
200 
21O 
220 
230 
240 
250 
260 
270 
280 
290 
3OO 


.09 


.393 
.787 
1.181 
1.574 
1.968 
2.362 
2.756 
3.149 
3.543 


.001 
002 
.003 


005 


007 
.008 
009 


.039 
.078 
.118 
.157 
.196 
.236 
.275 
.315 
.354 


B 
FEET 


.3281 
.6561 
.984 
1.312 
1.640 
1.968 
2.296 
2.624 
2.952 


.032 
.065 
.098 
.131 
.164 
.196 
.229 
.262 
.295 


C 

FEET  AND 
INCHES  TO 
NEAREST  Vs4 


Q-77/s" 


2-39/e  + 

2-71/*"- 

2m"+ 


r/; 

2" 

2% 


3%, 


.003 
.006 
.009 
.013 
.016 
.019 
.023 
.026 
.029 


'/13 
'/." 

y; 
v* 
1/{ 

y; 


1%'+ 


2% 


;;+3 


5/  " 
/32 

25/" 
/128 

15/" 
/64 

y* 


1 

3  Flc 
6no 

9 


o 


8S 


1 
2i 

F 
4C 


7m 


in  feet  and  inches  to  nearest  64th,  and  also  as  feet  and  decimal 

Fractions  of  meter  are  read  from  the  right  hand  portion  of  the 

0-11%"    .07  meter  =  2.756  in=.229  ft^O^K" 

To  convert  same  number  to  feet  and  inches:  147.000  m  =  482:3%" 

.6  «  =  l-H5/8 
.07  "  =  0-2M 
.008  "  =  0-0 Ke 


147.678  m  = 


264 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


aj 
3 

5 

^ 
31 

<  w 
Hg 

g 

en 

u 

= 
u 
fc 


^^  O5 


1^*  C^  t>* 


^H  ^H  rH  (N  (N  (N  CO 


<N  CO  CO  TlJ  rJJ  »O  10 
^  i-H  I-H  (N  (N  (N  <M 


t>-Cs5t>- 

00  O5  O5 


coo(N»oo 


O5I>*OCOi—  tOicOTtHfNO 
i—  ICO"—  ICO'—  iiOO»OOiO 


i-H  rH  i-l  i-H  (N  (N  (N 


I-H  cO  T— (  iO  O  iA 

O5  O5  O  O  TH  T-H  (N  (N  <N  CO 

'cot^oco'ooiiM'iooo 


'  CO  CO'  O5  (N  "5  00  ^H  r}H  00 
TH  I-H  T-I  C<l  (N  (N 


T-H  I-H  T—  i  (N 


co  co  os  <M'  10  oo  1-5  rj< 

T-H    T—  1    1—  1    O3    (N 


w 

CQ 

I* 

I 

g 
o 


1>» 
<N 


800t>-COiOCOC<l'-HOOOI>-CO»OCO(N'— • 
iCTHt^-COOJiOi— !I>(NOOTtiOcOC<IOO 

rtHiOt^OOO'— iCO*OcOOOO5i— ICO-<*ICO1> 


> 

I 


Soo 
T-< 


CO 
(N 


CO  "^ 


iOCOCJi—  tOOO 
i-tt^COO5iOO 


l>cOiOCO 


(M' 
O 


8O5l>- 
»Or-i 


S 
i 


i—  IOKOC01—  i 


COrHOOCOCO 


09.54  m 
of  the 


^§ 
II 

^ 

|i 
§1 

s  "I 


*OcOOOOi—  (CO^ 
(N(N(NCOCOCO  CO 


CO  COW*  T^ 


tely  only. 
ering  N 


im 
ngine 


Appr 
rom 


MISCELLANEOUS   TABLES   AND   DATA 


265 


TABLE  56 
CORRECTION  IN  FEET  FOR  CURVATURE  AND  REFRACTION 

(h  =  0.574  Z)2) 
D  =  Distance  in  miles 


Distance, 
in 
Miles 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1 

.6 

.7 

.8 

1.0 

1.1 

1.3 

1.5 

1.7 

1.9 

2.1 

2 

2.3 

2.5 

2.8 

3.0 

3.3 

3.6 

3.9 

4.2 

4.5 

4.8 

3 

5.2 

5.5 

5.9 

6.2 

6.6 

7.0 

7.4 

7.8 

8.3 

8.7 

4 

9.2 

9.6 

10.1 

10.6 

11.1 

11.6 

12.1 

12.7 

13.2 

13.8 

5 

14.3 

14.9 

15.5 

16.1 

16.7 

17.3 

18.0 

18.6 

19.3 

20.0 

6 

20.7 

21.4 

22.1 

22.8 

23.5 

24.2 

25.0 

25.7 

26.5 

27.3 

7 

28.1 

28.9 

29.8 

30.6 

31.4 

32.3 

33.2 

34.1 

35.0 

35.9 

8 

36.7 

37.6 

38.6 

39.5 

40.4 

41.4 

42.4 

43.4 

44.4 

45.5 

9 

46.5 

47.5 

48.6 

49.7 

50.7 

51.8 

52.9 

54.0 

55.1 

56.3 

10 

57.4 

58.6 

59.7 

60.9 

62.1 

63.3 

64.5 

65.7 

67.0 

68.2 

11 

69.5 

70.7 

71.9 

73.2 

74.5 

75.8 

77.1 

78.5 

79.8 

81.2 

12 

82.7 

84.0 

85.4 

86.8 

88.3 

89.7 

91.1 

92.6 

94.0 

95.5 

13 

97.0 

98.5 

100.0 

101.5 

103.1 

104.6 

106.2 

107.7 

109.3 

110.9 

14 

112.5 

114.1 

115.7 

117.4 

119.0 

120.7 

122.4 

124.0 

125.7 

127.4 

15 

129.1 

130.9 

132.6 

134.3 

136.1 

137.9 

139.7 

141.5 

143.3 

145.1 

16 

146.9 

148.7 

150.6 

152.5 

154.4 

156.3 

158.2 

160.1 

162.0 

163.9 

17 

165.8 

167.8 

169.8 

171.7 

173.7 

175.7 

177.7 

179.7 

181.8 

183.8 

18 

185.9 

188.0 

190.1 

192.2 

194.3 

196.4 

198.5 

200.7 

202.8 

205.0 

19 

207.1 

209.3 

211.5 

213.7 

216.0 

218.2 

220.4 

222.7 

224.9 

227.2 

20 

229.5 

231.8 

234.2 

236.5 

238.8 

241.2 

243.5 

245.9 

248.3 

250.7 

21 

253.1 

255.5 

257.9 

260.4 

262.8 

265.3 

267.7 

270.2 

272.7 

275.2 

22 

277.7 

280.3 

282.8 

285.4 

288.0 

290.5 

293.1 

295.7 

298.3 

301.0 

23 

303.6 

306.2 

308.9 

311.5 

314.2 

316.9 

319.6 

322.3 

325.0 

327.8 

24 

330.5 

333.3 

336.1 

338.9 

341.7 

344.5 

347.3 

350.1 

352.9 

355.8 

25 

358.6 

361.5 

364.4 

367.3 

370.2 

373.1 

376.0 

379.0 

381.9 

384.9 

26 

387.9 

390.9 

393.9 

396.9 

400.0 

403.0 

406.0 

409.1 

412.2 

415.3 

27 

418.3 

421.4 

424.5 

427.7 

430.8 

434.0 

437.1 

440.3 

443.5 

446.7 

28 

449.9 

453.1 

456.3 

459.6 

462.8 

466.1 

469.4 

472.7 

476.0 

479.3 

29 

482.6 

485.9 

489.3 

492.6 

496.0 

499.4 

502.8 

506.2 

509.6 

513.0 

30 

516.5 

519.9 

523.4 

526.8 

530.3 

533.8 

537.3 

540.8 

544.4 

547.9 

31 

551.5 

555.0 

558.6 

562.2 

565.8 

569.4 

573.0 

576.7 

580.3 

584.0 

32 

587.6 

591.3 

595.0 

598.7 

602.4 

606.1 

609.9 

613.6 

617.3 

621.1 

33 

624.9 

628.7 

532.5 

636.3 

640.2 

644.0 

647,9 

651.7 

655.6 

659.5 

34 

663.4 

667.3 

671.2 

675.1 

679.1 

683.0 

687.0 

690.9 

694.9 

698.9 

35 

702.9 

707.0 

711.0 

715.1 

719.1 

723.2 

727.3 

731.4 

735.5 

739.6 

36 

743.7 

747.8 

752.0 

756.1 

760.3 

764.5 

768.7 

772.9 

777.1 

781.3 

37 

785.6 

789.8 

794.1 

798.4 

802.6 

806.9 

811.3 

815.6 

819.9 

824.2 

38 

828.6 

833.0 

837.4 

841.8 

846.2 

850.6 

855.0 

859.4 

863.9 

868.3 

39 

872.8 

877.3 

881.8 

886.3 

890.8 

895.3 

899.9 

904.4 

909.0 

913.5 

40 

918.1 

922.7 

927.3 

931.9 

936.6 

941.2 

945.9 

950.5 

955.2 

959.9 

266 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


TABLE  57 
STADIA  TABLE 


Slant  Distance 

100 

200 

300 

400 

500 

600 

700 

800 

900 

0°       2'  .. 

0.06 

0.1 

0.2 

0.2 

0.3 

0.3 

0.4 

0.5 

0.5 

4  

0.12 

0.2 

0.3 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

6  

0.17 

0.3 

0.5 

0.7 

0.9 

1.0 

1.2 

1.4 

1.6 

8  

0.23 

0.5 

0.7 

0.9 

1.2 

1.4 

1.6 

1.9 

2.1 

10  

0.29 

0.6 

0.9 

1.2 

1.5 

1.7 

2.0 

2.3 

2.6 

12  

0.35 

0.7 

1.0 

1.4 

1.7 

2.1 

2.4 

2.8 

3.1 

14  

0.41 

0.8 

1.2 

1.6 

2.0 

2.4 

2.8 

3.3 

3.7 

16  

0.47 

0.9 

1.4 

1.9 

2.3 

2.8 

3.3 

3.7 

4.2 

18  

0.52 

.0 

1.6 

2.1 

2.6 

3.1 

3.7 

4.2 

4.7 

20  

0.58 

.2 

1.7 

2.3 

2.9 

3.5 

4.1 

4.6 

5.2 

22  

0.64 

.3 

1.9 

2.6 

3.2 

3.8 

4.5 

5.1 

5.8 

24  

0.70 

.4 

2.1 

2.8 

3.5 

4.2 

4.9 

5.6 

6.3 

26  

0.76 

.5 

2.3 

3.0 

3.8 

4.5 

5.3 

6.0 

6.8 

28  

0.81 

.6 

2.4 

3.2 

4.1 

4.9 

5.7 

6.5 

7.3 

30  

0.87 

.7 

2.6 

3.5 

4.4 

5.2 

6.1 

7.0 

7.8 

32  

0.93 

1.9 

2.8 

3.7 

4.6 

5.6 

6.5 

7.4 

8.4 

34  

0.99 

2.0 

3.0 

3.9 

4.9 

5.9 

6.9 

7.9 

8.9 

36  

1.05 

2.1 

3.1 

4.2 

5.2 

6.3 

7.3 

8.4 

9.4 

38  

.11 

2.2 

3.3 

4.4 

5.5 

6.6 

7.7 

8.8 

9.9 

40  

.16 

2.3 

3.5 

4.6 

5.8 

7.0 

8.1 

9.3 

10.5 

42  

.22 

2.4 

3.7 

4.9 

6.1 

7.3 

8.5 

9.8 

11.0 

44 

.28 

2.6 

3.8 

5.1 

6.4 

7.7 

9.0X 

10.2 

11.5 

46  

.34 

2.7 

4.0 

5.3 

6.7 

8.0 

9.4 

10.7 

12.0 

48  

.40 

2.8 

4.2 

5.6 

7.0 

8.4 

9.8 

11.2 

12.5 

50  ........ 

.45 

2.9 

4.4 

5.8 

7.2 

8.7 

10.2 

11.6 

13.1 

52  

•51 

3.0 

4.5 

6.0 

7.5 

9.1 

10.6 

12.1 

13.6 

54  

.57 

3.1 

4.7 

6.3 

7.8 

9.4 

11.0 

12.6 

14.1 

56  

.63 

3.3 

4.9 

6.5 

8.1 

9.8 

11.4 

13.0 

14.6 

58  

.69 

3.4 

5.0 

6.7 

8.4 

10.1 

11.8 

13.5 

15.2 

60  

.74 

3.5 

5.2 

7.0 

8.7 

10.5 

12.2 

14.0 

15.7 

10       2'  ... 

1.80 

3.6 

5.4 

7.2 

9.0 

10.8 

12.6 

14.4 

16.2 

4  

1.86 

3.7 

5.6 

7.4 

9.3 

11.2 

13.0 

14.9 

16.7 

6  

1.92 

3.8 

5.8 

7.7 

9.6 

11.5 

13.4 

15.4 

17.3 

8  

1.98 

4.0 

5.9 

7.9 

9.9 

11.9 

13.8 

15.8 

17.8 

10  

2.03 

4.1 

6.1 

8.1 

10.2 

12.2 

14.2 

16.3 

18.3 

12  .  ,  

2.09 

4.2 

6.3 

8.4 

10.5 

12.6 

14.7 

16.7 

18.8 

14  

2.15 

4.3 

6.5 

8.6 

10.8 

12.9 

15.1 

17.2 

19.4 

16  

2.21 

4.4 

6.6 

8.8 

11.0 

13.3 

15.5 

17.7 

19.9 

18  

2.27 

4.5 

6.8 

9.1 

11.3 

13.6 

15.9 

18.1 

20.4 

20  

2.33 

4.7 

7.0 

9.3 

11.6 

14.0 

16.3 

18.6 

20.9 

22  

2.38 

4.8 

7.2 

9.5 

11.9 

14.3 

16.7 

19.1 

21.5 

24  

2.44 

4.9 

7.3- 

9.8 

12.2 

14.7 

17.1 

19.5 

22.0 

26  

2.50 

5.0 

7.5 

10.0 

12.5 

15.0 

17.5 

20.0 

22.5 

28  

2.56 

5.1 

7.7 

10.2 

12.8 

15.3 

17.9 

20.5 

23.0 

30  

2.62 

5.2 

7.8 

10.5 

13.1 

15.7 

18.3 

20.9 

23.5 

32 

2.67 

5.3 

8.0 

10.7 

13.4 

16.0 

18.7 

21.4 

24.1 

34  

2.73 

5.5 

8.2 

10.9 

13.7 

16.4 

19.1 

21.9 

24.6 

36  

2.79 

5.6 

8.4 

11.2 

14.0 

16.7 

19.5 

22.3 

25.1 

38  

2.85 

5.7 

8.5 

11.4 

14.2 

17.1 

19.9 

22.8 

25.6 

40  

2.91 

5.8 

8.7 

11.6 

14.5 

17.4 

20.3 

23.3 

26.2 

42  

2.97 

5.9 

8.9 

11.9 

14.8 

17.8 

20.8 

23.7 

26.7 

44  

3.02 

6.0 

9.1 

12.1 

15.1 

18.1 

21.2 

24.2 

27.2 

46  

3.08 

6.2 

9.2 

12.3 

15.4 

18.5 

21.6 

24.6 

27.7 

48  

3.14 

6.3 

9.4 

12.6 

15.7 

18.8 

22.0 

25.1 

28.3 

50  

3.20 

6.4 

9.6 

12.8 

16.0 

19.2 

22.4 

25.6 

28.8 

52  

3.26 

6.5 

9.8 

13.0 

16.3 

19.5 

22.8 

26.0 

29.3 

54  

3.31 

6.6 

9.9 

13.2 

16.6 

19.9 

23.2 

26.5 

29.8 

56 

3.37 

6.7 

10.1 

13.5 

16.9 

20.2 

23.6 

27.0 

30.3 

58  

3.43 

6.9 

10.3 

13.7 

17.1 

20.6 

24.0 

27.4 

30.9 

60  

3.49 

7.0 

10.5 

14.0 

17.4 

20.9 

24.4 

27.9 

31.4 

Horizontal  dist. 

99.9 

199.8 

299.6 

399.5 

499.4 

599.3 

699.2 

799.0 

898.9 

MISCELLANEOUS   TABLES   AND   DATA 


267 


TABLE  57  (Continued] 
STADIA  TABLE 


Slant  Distance        100 

200 

300 

400 

500 

600 

700 

800 

900 

2°      2'  3.55 

7.1 

10.6 

14.2 

17.7 

21.3 

24.8 

28.4 

31.9 

4  3.60 

7.2 

10.8 

14.4 

18.0 

21.6 

25.2 

28.8 

32.4 

6  3.66 

7.3 

11.0 

14.6 

18.3 

22.0 

25.6 

29.3 

33.0 

8  3  .  72 

7.4 

11.2 

14.9 

18.6 

22.3 

26.0 

29.8 

33.5 

10  3.78 

7.6 

11.3 

15.1 

18.9 

22.7 

26.4 

30.2 

34.0 

12  3.84 

7.7 

11.5 

15.3 

19.2 

23.0 

26.9 

30.7 

34.5 

14  3.90 

7.8 

11.7 

15.6 

19.5 

23.4 

27.3 

31.2 

35.1 

16  3.95 

7.9 

11.9 

15.8 

19.8 

23.7 

27.7 

31.6 

35.6 

18  4.01 

8.0 

12.0 

16.0 

20.0 

24.1 

28.1 

32.1 

36.1 

20  4.07 

8.1 

12.2 

16.3 

20.3 

24.4 

28.5 

32.5 

36.6 

22  4.13 

8.3 

12.4 

16.5 

20.6 

24.8 

28.9 

33.0 

37.1 

24  4.18 

8.4 

12.6 

16.7 

20.9 

25.1 

29.3 

33.5 

37.7 

26  4.24 

8.5 

12.7 

17.0 

21.2 

25.5 

29.7 

33.9 

38.2 

28  4.30 

8.6 

12.9 

17.2 

21.5 

25.8 

30.1 

34.4 

38.7 

30  4.36 

8.7 

13.1 

17.4 

21.8 

26.1 

30.5 

34.9 

39.2 

32                     4  42 

8.8 

13.2 

17.7 

22.1 

26.5 

30.9 

35.3 

39.7 

34  4.47 

8.9 

13.4 

17.9 

22.4 

26.8 

31.3 

35.8 

40.3 

36  4.53 

9.1 

13.6 

18.1 

22.7 

27.2 

31.7 

36.3 

40.8 

38  '.  .     4.59 

9.2 

13.8 

18.4 

23.0 

27.5 

32.1 

36.7 

41.3 

40  4.65 

9.3 

13.9 

18.6 

23.2 

27.9 

32.5 

37.2 

41.8 

42  4.71 

9.4 

14.1 

18.8 

23.5 

28.2 

32.9 

37.6 

42.4 

44  4.76 

9.5 

14.3 

19.1 

23.8 

28.6 

33.3 

38.1 

42.9 

46  !    4.82 

9.6 

14.5 

19.3 

24.1 

28.9 

33.8 

38.6 

43.4 

48  4.88 

9.8 

14.6 

19.5 

24.4 

29.3 

34.2 

39.0 

43.9 

50  !    4.94 

9.9 

14.8 

19.8 

24.7 

29.6 

34.6 

39.5 

44.4 

52  5.00 

10.0 

15.0 

20.0 

25.0 

30.0 

35.0 

40.0 

45.0 

54  5.05 

10.1 

15.2 

20.2 

25.3 

30.3 

35.4 

40.4 

45.5 

56  5.11 

10.2 

15.3 

20.4 

25.6 

30.7 

35.8 

40.9 

46.0 

58  .  .      5.17 

10.3 

15.5 

20.7 

25.8 

31.0 

36.2 

41.4 

46.5 

60                      5  23 

10.5 

15.7 

20.9 

26.1 

31.4 

36.6 

41.8 

47.1 

Horizontal  dist.    99.7 

199.5 

299.2 

398.9 

498.7 

598.4 

698.1 

797.8 

897.5 

3°      2'  5.28 

10.6 

15.9 

21.1 

26.4 

31.7 

37.0 

42.3 

47.6 

4  5.34 

10.7 

16.0 

21.4 

26.7 

32.1 

37.4 

42.7 

48.1 

6  5.40 

10.8 

16.2 

21.6 

27.0 

32.4 

37.8 

43.2 

48.6 

8  5.46 

10.9 

16.4 

21.8 

27.3 

32.7 

38.2 

43.7 

49.1 

10  5.52 

11.0 

16.5 

22.1 

27.6 

33.1 

38.6 

44.1 

49.6 

12  5.57 

11.1 

16.7 

22.3 

27.9 

33.4 

39.0 

44.6 

50.2 

14  ..                 5  63 

11.3 

16.9 

22.5 

28.2 

33.8 

39.4 

45.0 

50.7 

16                      5  69 

11.4 

17.1 

22.8 

28.4 

34.1 

39.8 

45.5 

51.2 

18.  .......      5.75 

11.5 

17.2 

23.0 

28.7 

34.5 

40.2 

46.0 

51.7 

20  !    5.80 

11.6 

17.4 

23.2 

29.0 

34.8 

40.6 

46.4 

52.2 

22  i    5.86 

11.7 

17.6 

23.4 

29.3 

35.1 

41.0 

46.9 

52.8 

24  5.92 

11.8 

17.8 

23.7 

29.6 

35.5 

41.4 

47.4 

53.3 

26  5.98 

12.0 

17.9 

23.9 

29.9 

35.9 

41.8 

47.8 

53.8 

28  6.04 

12.1 

18.1 

24.1 

30.2 

36.2 

42.2 

48.3 

54.3 

30  ;    6.09 

12.2 

18.3 

24.4 

30.5 

36.6 

42.6 

48.7 

54.8 

32  6.15 

12.3 

18.4 

24.6 

30.8 

36.9 

43.0 

49.2 

55.4 

34  6.21 

12.4 

18.6 

24.8 

;  31.0 

37.3 

43.5 

49.7 

55.9 

36  6.27 

12.5 

18.8 

25.1 

31.3 

37.6 

43.9 

50.1 

56.4 

38  3.32 

12.6 

19.0 

25.3 

31.6 

37.9 

44.3 

50.6 

56.9 

40  3.38 

12.8 

19.1 

25.5 

31.9 

38.3 

44.7 

51.1 

57.4 

'42  6.44 

12.9 

19.3 

25.8 

32.2 

38.6 

45.1 

51.5 

58.0 

44                       6  50 

13.0 

19.5 

26.0 

32.5 

39.0 

45.5 

52.0 

58.5 

46  6.55 

13.1 

19^7 

26^2 

32^8 

39.3 

45.9 

52.4 

59.0 

48  S.61 

13.2 

19.8 

26.4 

33.1 

39.7 

46.3 

52.9 

59.5 

50  6.67 

13.3 

20.0 

26.7 

33.4 

40.0 

46.7 

53.4 

60.0 

52  6  .  73 

13.5 

20.2 

26.9 

33.6 

40.4 

47.1 

53.8 

60.6 

54  6.78 

13.6 

20.4 

27.1 

33.9 

40.7 

47.5 

54.3 

61.1 

56  6.84 

13.7 

20.5 

27.4 

34.2 

41.1 

47.9 

54.7 

61.6 

58                      6  90 

13.8 

20.7 

27.6 

34.5 

41.4 

48.3 

55.2 

62.1 

60  6.96 

13.9 

20.9 

27  '.8 

34^8 

4l!? 

48!7 

55.7 

62.6 

Horizontal  dist.    99.5 

199  0 

298.5 

398.0 

497.6 

597.1 

696.6 

796.1 

895.6 

268 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


TABLE   57  (Continued) 
STADIA  TABLE 


Slant  Distance 

100 

200 

300 

400 

500 

600 

700 

800 

900 

A°       2'  
4         4  
6  
8  

7.02 
7.07 
7.13 
7.19 

14.0 
14.1 
14.3 
14.4 

21.0 
21.2 
21.4 
21.6 

28.1 
28.3 
28.5 

28.8 

35.1 

35.4 
35.7 
35.9 

42.1 

42.4 
42.8 
43.1 

49.1 
49.5 
49.9 
50.3 

56.1 
56.6 
57.0 
57.5 

63.1 
63.7 
64.2 
64.7 

10  
12  
14  
16  
18 

7.25 
7.30 
7.36 

7.42 
7.48 

14.5 
14.6 
14.7 
14.8 
15.0 

21.7 
21.9 
22.1 
22.3 
22.4 

29.0 
29.2 
29.4 
29.7 
29.9 

36.2 
36.5 
36.8 
37.1 
37.4 

43.5 
43.8 
44.2 
44.5 
44  9 

50.7 
51.1 
51.5 
51.9 
52  3 

58.0 
58.4 
58.9 
59.3 
59  8 

65.2 
65.7 
66.2 
66.8 
67  3 

20 

7.53 

15.1 

22.6 

30.2 

37  7 

45  2 

52  7 

60  3 

67  8 

22 

7.59 

15  2 

22  8 

30.4 

38  0 

45  5 

53  1 

60  7 

68  3 

24 

7  65 

15  3 

22  9 

30  6 

OQ     O 

45  9 

53  5 

61  2 

68  8 

26  
28  
30  
32  
34  
36  
38  
40  
42  
44  
46  
48 

7.71 

7.76 
7.82 
7.88 
7.94 
7.99 
8.05 
8.11 
8.17 
8.22 
8.28 
8  34 

15.4 
15.5 
15.6 
15.8 
15.9 
16.0 
16.1 
16.2 
16.3 
16.4 
16.6 
16  7 

23.1 
23.3 
23.5 
23.6 
23.8 
24.0 
24.2 
24.3 
24.5 
24.7 
24.8 
25  0 

30.8 
31.1 
31.3 
31.5 
31.7 
32.0 
32.2 
32.4 
32.7 
32.9 
33.1 
33  4 

38.5 
38.8 
39.1 
39.4 
39.7 
40.0 
40.3 
40.5 
40.8 
41.1 
41.4 
41  7 

46.2 
46.6 
46.9 
47.3 
47.6 
48.0 
48.3 
48.6 
49.0 
49.3 
49.7 
50  0 

53.9 
54.3 
54.7 
55.1 
55.5 
56.0 
56.4 
56.8 
57.2 
57.6 
58.0 
58  4 

81.6 
62.1 
62.6 
63.0 
63.5 
63.9 
64.4 
64.9 
65.3 
65.8 
66.2 
66  7 

69.3 
69.9 
70.4 
70.9 
71.4 
71.9 
72.5 
73.0 
73.5 
74.0 
74.5 
75  0 

50  
52  
54  
56  
58  
60  

8.40 
8.45 
8.51 
8.57 
8.63 
8  68 

16.8 
16.9 
17.0 
17.1 
17.3 
17  4 

25.2 
25.4 
25.5 
25.7 
25.9 
26  0 

33.6 
33.8 
34.0 
34.3 
34.5 
34.7 

42.0 
42.3 
42.6 
42.8 
43.1 
43  4 

50.4 
50.7 
51.1 
51.4 
51.8 
52  1 

58.8 
59.2 
59.6 
60.0 
60.4 
60  8 

67.2 
67.6 
68.1 
68.5 
69.0 
69  5 

75.6 
76.1 
76.6 
77.1 
77.6 
78  1 

Horizontal  dist. 

*°     2'  

O         4  

99.2 

8.74 
8.80 

198.5 

17.5 
17.6 

297.7 

26.2 
26.4 

397.0 

35.0 
35  2 

496.2 

43.7 
44.0 

595.4 

52.4 
52  8 

694.7 

61.2 
61  6 

793.9 

69.9 
70  4 

893.0 

78.7 
79.2 

6  

8.85 

17.7 

26  6 

35  4 

44  3 

53  1 

62  0 

70  8 

79.7 

8  
10  
12  
14  
16  
18  
20  
22 

8.91 
8.97 
9.03 
9.08 
9.14 
9.20 
9.25 
9  31 

17.8 
17.9 
18.1 
18.2 
18.3 
18.4 
18.5 
18  6 

26.7 
26.9 
27.1 
27.2 
27.4 
27.6 
27.8 
27  9 

35.6 
35.9 
36.1. 
36.3 
36.6 
36.8 
37.0 
37  2 

44.6 
44.8 
45.1 
45.4 
45.7 
46.0 
46.3 
46  6 

53.5 
53.8 
54.2 
54.5 
54.8 
55.2 
55.5 
55  9 

62.4 
62.8 
63.2 
63.6 
64.0 
64.4 
64.8 
65  2 

71.3 
71.7 

72.2 
72.7 
73.1 
73.6 
74.0 
74  5 

80.2 
80.7 
81.2 
81.7 
82.3 
82.8 
83.3 
83  8 

24 

9  37 

18  7 

28  1 

37  5 

46  8 

56  2 

65  6 

74  9 

84  3 

26  
28  

9.43 
9.48 

18.9 
19.0 

28.3 

28  4 

37.7 
37  9 

47.1 
47.4 

56.6 
56  9 

66.0 
66  4 

75.4 
75.9 

84.8 
85.3 

30  
32  
34  
36  
38  
40  
42 

9.54 
9.60 
9.65 
9.71 
9.77 
9.83 
9  88 

19.1 
19.2 
19.3 
19.4 
19.5 
19.7 
19  8 

28.6 
28.8 
29.0 
29.1 
29.3 
29.5 
29  6 

38.2 
38.4 
38.6 
38.8 
39.1 
39.3 
39  5 

47.7 
48.0 
48.3 
48.6 
48.8 
49.1 
49  4 

57.2 
57.6 
57.9 
58.3 
58.6 
59.0 
59  3 

66.8 
67.2 
67.6 
68.0 
68.4 
68.8 
69  2 

76.3 
76.8 
77.2 
77.7 
78.1 
78.6 
79  0 

85.9 
86.4 
86.9 
87.4 
87.9 
88.4 
88  "9 

44 

9  94 

19  9 

29  8 

39  8 

49  7 

59  6 

69  6 

79  5 

89  4 

46  

10.00 

20.0 

30  0 

40  0 

50  0 

60  0 

70  0 

80  0 

90.0 

48  

10.05 

20  1 

30  2 

40  2 

50  3 

60  3 

70  4 

80  4 

90.5 

50  
52  
54  
56  
58  
60  
Horizontal  dist. 

10.11 
10.17 
10.22 
10.28 
10.33 
10.40 
98.9 

20.2 
20.3 
20.4 
20.6 
20.7 
20.8 
197.8 

30.3 
30.5 
30.7 
30.8 
31.0 
31.2 
296.7 

40.4 
40.7 
40.9 
41.1 
41.4 
41.6 
395.6 

50.5 
50.8 
51.1 
51.4 
51.7 
52.0 
494.5 

60.7 
61.0 
61.3 
61.7 
62.0 
62.4 
593.5 

70.8 
71.2 
71.6 
72.0 
72.4 
72.8 
692.4 

80.9 
81.3 
81.8 
82.2 
82.7 
83.2 
791.3 

91.0 
91.5 
92.0 
92.5 
93.0 
93.6 
890.2 

MISCELLANEOUS   TABLES   AND   DATA 


269 


TABLE  57  (Continued] 
STADIA  TABLE 


Slant  Distance 

100 

200 

300 

400 

500 

600 

700 

800 

900 

60       2' 

10.45 

20.9 

31.4 

41.8 

52.3 

62.7 

73.2 

83.6 

94.1 

4::.:::.. 

10.51 

21.0 

31.5 

42.0 

52.5 

63.1 

73.6 

84.1 

94.6 

6  
8  
10  
12 

10.57 
10.62 
10.68 
10.74 

21.1 
21.2 
21.4 
21.5 

31.7 
31.9 
32.0 
32.2 

42.3 

42.5 
42.7 
42.9 

52.8 
53.1 
53.4 
53.7 

63.4 
63.7 
64.0 
64.4 

74.0 
74.4 
74.8 
75.2 

84.5 
85.0 
85.4 
85.9 

95.1 
95.6 
96.1 
96.6 

14 

10  79 

21.6 

32.4 

43.2 

54.0 

64.8 

75.5 

86.3 

97.1 

16  

10.85 

21.7 

32.5 

43.4 

54.2 

65.1 

75.9 

'86.8 

97.6 

18  
20  
22  
24 

10.91 
10.96 
11.02 
11  08 

21.8 
21.9 
22.0 
22.2 

32.7 
32.9 
33.1 
33.2 

43.6 
43.8 
44.1 
44.3 

54.5 
54.8 
55.1 
55.4 

65.4 
65.8 
66.1 
66.5 

76.3 
76.7 
77.1 

77.5 

87.2 
87.7 
88.2 
88.6 

98.2 
98.7 
99.2 
99.7 

26  

11.13 

22.3 

33.4 

44.5 

55.6 

66.8 

77.9 

89.1 

100.2 

28  
30  
32  
34 

11.19 
11.25 
11.30 
11  36 

22.4 
22.5 
22.6 
22.7 

33.6 
33.7 
33.9 
34.1 

44.8 
45.0 
45.2 
45.4 

55.9 
56.2 
56.5 
56.8 

67.1 
67.5 
67.8 
68.2 

78.3 
78.7 
79.1 
79.5 

89.5 
90.0 
90.4 
90.9 

100.7 
101.2 
101.7 
102.2 

36  
38  

11.42 
11.47 

22.8 
22.9 

34.2 
34.4 

45.7 
45.9 

57.1 
57.4 

68.5 
68.8 

79.9 
80.3 

91.3 
91.8 

102.7 
103.2 

40  
42  
44  
46  
48  
50  
52  
54  
56  
58  
60  
Horizontal  dist. 

ry°      2'  
1           4.  
6      .. 

11.53 
11.59 
11.64 
11.70 
11.76 
11.81 
11.87 
11.93 
11.98 
12.04 
12.10 
98.5 

12.15 
12.21 
12  26 

23.1 
23.2 
23.3 
23.4 
23.5 
23.6 
23.7 
23.9 
24.0 
24.1 
24.2 
197.0 

24.3 
24.4 
24  5 

34.6 
34.8 
34.9 
35.1 
35.3 
35.4 
35.6 
35.8 
35.9 
36.1 
36.3 
295.5 

36.5 
36.6 
36  8 

46.1 
46.3 
46.6 
46.8 
47.0 
47.2 
47.5 
47.7 
47.9 
48.2 
48.4 
394.0 

48.6 
48.8 
49  1 

57.6 
57.9 
58.2 
58.5 
58.8 
59.1 
59.3 
59.6 
59.9 
60.2 
60.5 
492.6 

60.8 
61.0 
61  3 

69.2 
69.5 
69.9 
70.2 
70.5 
70.9 
71.2 
71.6 
71.9 
72.2 
72.6 
591.1 

72.9 
73.2 
73  6 

80.7 
81.1 
81.5 
81.9 
82.3 
82.7 
83.1 
83.5 
83.9 
84.3 
84.7 
689.6 

85.1 
85.5 
85  8 

92.2 
92.7 
93.1 
93.6 
94.0 
94.5 
95.0 
95.4 
95.9 
96.3 
96.8 
788.1 

97.2 
97.7 
98  1 

103.8 
104.3 
104.8 
105.3 
105.8 
106.3 
106.8 
107.3 
107.8 
108.4 
108.9 
886.6 

109.4 
109.9 
110.4 

8  
10  
12  

12.32 
12.38 
12.43 

24.6 
24.8 
24.9 

37.0 
37.1 
37.3 

49.3 
49.5 
49.7 

61.6 
61.9 
62.2 

73.9 
74.3 
74.6 

86.2 
86.6 
87.0 

98.6 
99.0 
99.5 

110.9 
111.4 
111.9 

14  

12.49 

25.0 

37.5 

50.0 

62.4 

74.9 

87.4 

99.9 

112.4 

16  
18    .. 

12.55 
12  60 

25.1 
25  2 

37.6 
37  8 

50.2 
50  4 

62.7 
63  0 

75.3 
75  6 

87.8 
88.2 

100.4 
100  8 

112.9 
113.4 

20  
22  
24  
26  
28  
30    .. 

12.66 
12.71 
12.77 
12.83 
12.88 
12  94 

25.3 
25.4 
25.5 
25.7 

25.8 
25  9 

38.0 
38.1 
38.3 
38.5 
38.6 
38  8 

50.6 
50.9 
51.1 
51.3 
51.5 
51  8 

63.3 
63.6 
63.8 
64.1 
64.4 
64  7 

75.9 
76.3 
76.6 
77.0 
77.3 
77  6 

88.6 
89.0 
89.4 
89.8 
90.2 
90  6 

101.3 
101.7 
102.2 
102.6 
103.1 
103  5 

113.9 
114.4 
114.9 
115.4 
115.9 
116  4 

32  
34  
36  
38  
40  
42  
44 

13.00 
13.05 
13.11 
13.16 
13.22 
13.28 
13  33 

26.0 
26.1 
26.2 
26.3 
26.4 
26.6 
26  7 

39.0 
39.2 
39.3 
39.5 
39.7 
39.8 
40  0 

52.0 
52.2 
52.4 
52.7 
52.9 
53.1 
53  3 

65.0 
65.3 
65.5 
65.8 
66.1 
66.4 
66  7 

78.0 
78.3 
78.6 
79.0 
79.3 
79.7 
80  0 

91.0 
91.4 
91.7 
92.1 
92.5 
92.9 
93  2 

104.0 
104.4 
104.9 
105.3 
105.8 
106.2 
106  7 

117.0 
117.5 
118.0 
118.5 
119.0 
119.5 
120.0 

46  
48  
50  .... 

13.39 
13.44 
13.50 

26.8 
26.9 
27  0 

40.2 
40.3 
40  5 

53.6 
53.8 
54  0 

66.9 
67.2 
67  5 

80.3 
80.7 
81  0 

93.7 
94.1 
94  5 

107.1 
107.6 
108.0 

120.5 
121.0 
121.5 

52  
54  
56  
58  
60  

13.56 
13.61 
13.67 
13.73 
13.78 

27.1 
27.2 
27.3 
27.5 
27.6 

40.7 
40.8 
41.0 
41.2 
41.3 

54.2 
54.5 
54.7 
54.9 
55.1 

67.8 
68.1 
68.3 
68.6 
68.9 

81.3 
81.7 
82.0 
82.3 
82.7 

94.9 
95.3 
95.7 
96.1 
96.4 

108.5 
108.9 
109.4 
109.8 
110.3 

122.0 
122.5 
123.0 
123.5 
124.0 

Horizontal  dist. 

98.1 

196.1 

294.2 

392.2 

490.3 

588.4 

686.4 

784.5 

882.6 

270 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


TABLE  57  (Continued] 
STADIA  TABLF 


Slant  Distance 

100 

200 

300 

400 

500 

600 

700 

800 

900 

80      5'  

13.92 

27.8 

41.8 

55.7 

69.6 

83  5 

97  4 

111  4 

125  3 

10    
15 

14.06 
14  20 

28.1 
28  4 

42.2 
42  6 

56.2 
56  8 

70.3 
71  0 

84.4 
85  2 

98.4 
99  4 

112.5 
113  6 

126.6 
127  8 

20  
25  
30  
35  
40  
45  
50  
55  
60 

14.34 
14.48 
14.62 
14.76 
14.90 
15.04 
15.17 
15.31 
15  45 

28.7 
29.0 
29.2 
29.5 
29.8 
30.1 
30.3 
30.6 
30  9 

43.0 
43.4 
43.9 
44.2 
44.7 
45.1 
45.5 
45.9 
46  4 

57.4 
57.9 
58.5 
59.0 
59.6 
60.1 
60.7 
61.2 
61  8 

71.7 
72.4 
73.1 
73.7 
74.5 
75.2 
75.9 
76.6 
77  3 

86.0 
86.9 
87.7 
88.4 
89.4 
90.2 
91.0 
91.9 
92  7 

100.4 
101.4 
102.3 
103.1 
104.3 
105.2 
106.2 
107.2 
108  2 

114.7 
115.8 
116.9 
117.8 
119.2 
120.3 
121.4 
122.5 
123  6 

129.1 
130.3 
131.6 
132.5 
134.1 
135.3 
136.6 
137.8 
139  1 

Horizontal  dist. 
Q°      5'  

y  10  

15  
20  
25  
30  
35  
40  
45 

97.5 

15.59 
15.73 
15.86 
16.00 
16.14 
16.28 
16.42 
16.55 
16  69 

195.1 

31.2 
31.5 
31.7 
32.0 
32.3 
32.6 
32.8 
33.1 
33  4 

292.7 

46.8 
47.2 
47.6 
48.0 
48.4 
48.8 
49.2 
49.7 
50  1 

390.2 

62.4 
62.9 
63.5 
64.0 
64.6 
65.1 
65.7 
66.2 
66  8 

487.8 

77.9 
78.6 
79.3 
80.0 
80.7 
81.4 
82.1 
82.8 
83  5 

585.3 

93.5 
94.5 
95.2 
96.0 
96.8 
97.7 
98.5 
99.3 
100  1 

682.9 

109.1 
110.2 
111.1 
112.0 
113.0 
113.9 
114.9 
115.9 
116  8 

780.4 

124.7 
125.9 
126.9 
128.0 
129.0 
130.2 
131.3 
132.4 
133  5 

878.0 

140.3 
141.6 
142.8 
144.0 
145.3 
146.5 
147.7 
148.0 
150  2 

50 

16  83 

33  7 

50  5 

67  3 

84  4 

101  0 

117  8 

134  6 

151  4 

55 

16  96 

33  9 

50  9 

67  9 

84  8 

101  8 

118  7 

135  7 

152  7 

60  

17.10 

34.2 

51.3 

68.4 

85.5 

102.6 

119.7 

136.8 

153.9 

Horizontal  dist. 
1A°      5'  

1U    10  

15  
20  
25 

97.0 

17.24 
17.37 
17.51 
17.65 
17  78 

194-.  0 

34.5 
34.7 
35.0 
35.3 
35  6 

291.0 

51.7 
52.1 
52.5 
52.9 
53.3 

387.9 

68.9 
69.5 
70.0 
70.6 
71  1 

484.9 

86.2 
86.9 
87.6 
88.2 
88  9 

581.9 

103.4 
104.2 
105.1 
105.9 
106  7 

678.9 

120.7 
121.6 
122.6 
123.5 
124  5 

775.9 

137.9 
139.0 
140.1 
141.2 
142  3 

872.9 

155.1 
156.4 
157.6 
158.8 
160  0 

30 

17  92 

35  8 

53  8 

71  7 

89  6 

107  5 

125  4 

143  3 

161  3 

35  

18.05 

36.1 

54.2 

72.2 

90.3 

108.3 

126.4 

144.4 

162.5 

40  
45  
50  
55  
60  

18.19 
18.37 
18.46 
18.60 
18.73 

36.4 
36.6 
36.9 
37.2 
37.5 

54.6 
55.0 
55.4 
55.8 
56.2 

72.7 
73.4 
73.8 
74.4 
74.9 

90.9 
91.8 
92.3 
93.0 
93.7 

109.1 
110.1 
110.8 
111.6 
112.4 

127.3 
128.5 
129.2 
130.2 
131.1 

145.5 
146.6 

147.7 
148.8 
149.8 

163.7 
165.3 
166.1 
167.4 
168.5 

Horizontal  dist. 

n°      5'  
10  
15  
20  
25  
30  
35  
40  
45  
50 

96.4 

18.86 
19.00 
19.13 
19.27 
19.40 
19.54 
19.67 
19.80 
19.94 
20  07 

192.7 

37.7 
38.0 
38.3 
38.5 
38.8 
39.1 
39.3 
39.6 
39.9 
40  1 

289.1 

56.6 
57.0 
57.4 
57.8 
58.2 
58.6 
59.0 
59.4 
59.8 
60  2 

385.4 

75.5 

76.0 
76.5 
77.1 
77.6 
78.1 
78.7 
79.2 
79.7 
80  3 

481.8 

94.3 
95.0 
95.7 
96.3 
97.0 
97.7 
98.4 
99.0 
99.7 
100  4 

578.2 

113.2 
114.0 
114.8 
115.6 
116.4 
117.2 
118.0 
118.8 
119.6 
120  4 

684.5 

132.1 
133.0 
133.9 
134.9 
135.8 
136.8 
137.7 
138.6 
139.6 
140  5  1 

770.9 

150.9 
152.0 
153.1 
154.1 
155.2 
156.3 
157.4 
158.4 
159.5 
160  6 

867.7 

169.8 
171.0 
172.2 
173.4 
174.6 
175.8 
177.0 
178.2 
179.4 
180  6 

55  
60  
Horizontal  dist. 

20.20 
20.34 
95.7 

40.4 
40.7 
191.3 

60.6 
61.0 
287.0 

80.8 
81.4 
382.7 

101^7 
478.4 

121.2 
122.0 
474.1 

141.4 
142.4 
669.7 

161.6 
162.7 
765.4 

181.8 
183.0 
861.1 

MISCELLANEOUS   TABLES   AND   DATA 


271 


TABLE  57  (Continued] 
STADIA  TABLE 


Slant  Distance 

100 

200 

300 

400 

500 

600 

700 

800 

900 

-g  o°      5' 

20.47 

40.9 

61.4 

81.9 

102.3 

122.8 

143.3 

163.8 

184.2 

12  i0:.. 

20.60 

41.2 

61.8 

82.4 

103.0 

123.6 

144.2 

164.8 

185^4 

15  

20.73 

41.5 

62.2 

82.9 

103.7 

124.4 

145.1 

165.9 

186.6 

20  

20.87 

41.7 

62.6 

83.5 

104.3 

125.2 

146.1 

166.9 

187.8 

25  

21.00 

42.0 

63.0 

84.0 

105.0 

126.0 

147.0 

168.0 

189.0 

30  

21.13 

42.3 

63.4 

84.5 

105.7 

126.8 

147.9 

169.0 

190.2 

35  

21.26 

42.5 

63.8 

85.1 

106.3 

127.6 

148.8 

170.1 

191.4 

40  

21.39 

42.8 

64.2 

85.6 

107.0 

128.4 

149.8 

171.2 

192.5 

45  

21.52 

43.1 

64.6 

86.1 

107.6 

129.2 

150.7 

172.2 

193.7 

50  

21.66 

43.3 

65.0 

86.6 

108.3 

129.9 

151.6 

173.2 

194.9 

55  

21.79 

43.6 

65.4 

87.2 

108.9 

130.7 

152.5 

174.3 

196.1 

60  

21.92 

43.8 

65.7 

87.7 

109.6 

131.5 

153.4 

175.3 

197.3 

Horizontal  dist. 

94.9 

189.9 

284.8 

379.8 

474.7 

569.6 

664.6 

759.5 

854.5 

1Q°      5' 

1  0      10  

22.05 
22.18 

44.1 
44.4 

66.1 
66.5 

88.2 
88.7 

110.2 
110.9 

132.3 
133.1 

154.3 
155.3 

176.3 
177.4 

198.4 
199.6 

15  

22.31 

44.6 

66.9 

89.2 

111.6 

133.9 

156.2 

178.5 

200.8 

20  

22.44 

44.9 

67.3 

89.8 

112.2 

134.6 

157.1 

179.5 

202.0 

25  

22.57 

45.1 

67.7 

90.3 

112.8 

135.4 

158.0 

180.6 

203.1 

30  

22.70 

45.4 

68.1 

90.8 

113.5 

136.2 

158.9 

181.6 

204.3 

35  

22.83 

45.7 

68.5 

91.3 

114.1 

137.0 

159.8 

182.6 

205.5 

40  

22.96 

45.9 

68.9 

91.8 

114.8 

137.7 

160.7 

183.7 

206.6 

45  

23.09 

46.2 

69.3 

92.4 

115.4 

138.5 

161.6 

184.7 

207.8 

50  

23.22 

46.4 

69.6 

92.9 

116.1 

139.3 

162.5 

185.7 

208.9 

55  

23.35 

46.7 

70.0 

93.4 

116.7 

140.1 

163.4 

186.8 

210.1 

60  

23.47 

46.9 

70.4 

93.9 

117.4 

140.8 

164.3 

187.8 

211.3 

Horizontal  dist. 

94.2 

188.3 

282.4 

376.6 

470.7 

564.9 

659.0 

753.2 

847.3 

U°      5'  
10  

23.60 
23.73 

47.2 

47.5 

70.8 
71.2 

94.4 
94.9 

118.0 
118.6 

141.6 
142.4 

165.2 
166.1 

188.8 
189.8 

212.4 
213.6 

15  

23.86 

47.7 

71.6 

95.4 

119.3 

143.2 

167.0 

190.9 

214.7 

20  

23.99 

48.0 

72.0 

95.9 

119.9 

143.9 

167.9 

191.9 

215.9 

25  

24.11 

48.2 

72.3 

96.5 

120.6 

144.7 

168.8 

192.9 

217.0 

30 

24.24 

48.5 

72.7 

97.0 

121.2 

145.4 

169.7 

193.9 

218  2 

35 

24.37 

48.7 

73.1 

97.5 

121.8 

146.2 

170.6 

194  9 

219  3 

40  

24.49 

49.0 

73.5 

9s!o 

122^5 

147.0 

171.5 

196.0 

220.4 

45  

24.62 

49.2 

73.9 

98.5 

123.1 

147.7 

172.3 

197.0 

221.6 

50  

24.75 

49.5 

74.2 

99.0 

123.7 

148.5 

173.2 

198.0 

222.7 

55  

24.87 

49.7 

74.6 

99.5 

124  .4 

149.2 

174.1 

199.0 

223.9 

60  

25.00 

50.0 

75.0 

100.0 

125.0 

150.0 

175.0 

200.0 

225.0 

Horizontal  dist. 

93.3 

186.6 

279.9 

373.2 

466.5 

559.8 

683.1 

786.4 

839.7 

iff:0    5'  

25.13 

50.3 

75.4 

100.5 

125.6 

150.8 

175.9 

201.0 

226.1 

1  0     10  

25.25 

50.5 

75.8 

101.0 

126.3 

151.5 

176.8 

202.0 

227.3 

15  

25.38 

50.8 

76.1 

101.5 

126.9 

152.3 

177.6 

203.0 

228.4 

20  ...... 

25.50 

51.0 

76.5 

102.0 

127.5 

153.0 

178.5 

204.0 

229.5   ' 

25  

25.63 

51.3 

76.9 

102.5 

128.1 

153.8 

179.4 

205.0 

230.6 

30  

25.75 

51.5 

77.3 

103.0 

128.8 

154.5 

180.3 

206.0 

231.8 

35  

25.88 

51.8 

77.6 

103.5 

129.4 

155.3 

181.1 

207.0 

232.9 

40  

26.00 

52.0 

78.0 

104.0 

130.0 

156.0 

182.0 

208.0 

234.0 

45  

26.12 

52.2 

78.4 

104.5 

130.6 

156.7 

182.9 

209.0 

235.1 

50  

26.25 

52.5 

78.7 

105.0 

131.2 

157.5 

183.7 

210.0  | 

236.2 

55 

26.37 

52.7 

79.1 

105.5 

131  9 

158  2 

184  6 

mo 

007     A 

60 

26.50 

53.0 

79.5 

106.0 

132  5 

159  0 

185  5 

.  U     i 

919   0 

£t&  t  .  *± 
oqo    c 

Horizontal  dist. 

92.4 

184.8 

277  .'2 

M9.« 

462.0 

554.4 

646  !  8 

£  l£  .  U       ! 

739.2 

Zoo  .  O 

831.6 

272 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


TABLE  57  (Concluded) 
STADIA  TABLE. 


Slant  Distance 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1  /?°      5' 

26.62 

53.2 

79.9 

106.5 

133.1 

159.7 

186.3 

213.0 

239.6 

16   10 

26.74 

53.5 

80.2 

107.0 

133.7 

160.5 

187.2 

213.9 

240.7 

15  

26.86 

53.7 

80.6 

107.5 

134.3 

161.2 

188.0 

214.9 

241.8 

20  

26.99 

54.0 

81.0 

108.0 

134.9 

161.9 

188.9 

215.9 

242.9 

25  

27.11 

54.2 

81.3 

108.4 

135.6 

162.7 

189.8 

216.9 

244.0 

30  

27.23 

54.5 

81.7 

108.9 

136.2 

163.4 

190.6 

217.9 

245.1 

35  

27.35 

54.7 

82.1 

109.4 

136.8 

164.1 

191.5 

218.8 

246.2 

40  

27.48 

55.0 

82.4 

109.9 

137.4 

164.9 

192.4 

219.8 

247.3 

45 

27.60 

55.2 

82.8 

110.4 

138.0 

165.6 

193.2 

220.8 

248.4 

50  

27.72 

55.4 

83.2 

110.9 

138.6 

166.3 

194.0 

221.7 

249.5 

55  

27.84 

55.7 

83.5 

111.4 

139.2 

167.0 

194.9 

222.7 

250.6 

60 

27.96 

55.9 

83.9 

111.8 

139.8 

167.8 

195.7 

223.7 

251.6 

Horizontal  dist. 

91.4 

183 

274 

366 

457 

549 

640 

732 

823 

17°    5'  

1  |        10  

28.08 
28.20 

56.2 
56.4 

84.2 
84.6 

112.3 
112.8 

140.4 
141.0 

168.5 
169.2 

196.6 
197.4 

224.6 
225.6 

252.7 
253.8 

15  

28.32 

56.6 

85.0 

113.3 

141.6 

169.9 

198.2 

226.6 

254.9 

20  

28.44 

56.9 

85.3 

113.8 

142.2 

170.6 

199.1 

227.5 

256.0 

25  

28.56 

57.1 

85.7 

114.2 

142.8 

171.4 

199.9 

228.5 

257.0 

30  

28.68 

57.4 

86.0 

114.7 

143.4 

172.1 

200.8 

229.4 

258.1 

35  

28.80 

57.6 

86.4 

115.2 

144.0 

172.8 

201.6 

230.4 

259.2 

40  

28.92 

57.8 

86.7 

115.7 

144.6 

173.5 

202.4 

231.3 

260.2 

45  

29.04 

58.1 

87.1 

116.1 

145.2 

174.2 

203.2 

232.3 

261.3 

50  

29.15 

58.3 

87.5 

116.6 

145.8 

174.9 

204.1 

233.2 

262.4 

55  

29.27 

58.5 

87.8 

117.1 

146.4 

175.6 

204.9 

234.2 

263.4 

60  

29.39 

58.8 

88.2 

117.6 

146.9 

176.3 

205.7 

235.1 

264.5 

Horizontal  dist. 

90.4 

181 

271 

362 

452 

543 

633 

724 

814 

1  O°      5'.  .  . 

29.51 

59.0 

88.5 

118.0 

147.5 

177.0 

206.5 

236.1 

265.6 

18    10  

29.62 

59.2 

88.9 

118.5 

148.1 

177.7 

207.4 

237.0 

266.6 

15  

29.74 

59.5 

89.2 

119.0 

148.7 

178.4 

208.2 

237.9 

267.7 

20  

29.86 

59.7 

89.6 

119.4 

149.3 

179.1 

209.0 

238.9 

268.7 

25  

29.97 

59.9 

89.9 

119.9 

149.9 

179.8 

209.8 

239.8 

269.8 

30  

30.09 

60.2 

90.3 

120.4 

150.5 

180.5 

210.6 

240.7 

270.8 

35  

30.21 

60.4 

90.6 

120.8 

151.0 

181.2 

211.4 

241.7 

271.9 

40  

30.32 

60.6 

91.0 

121.3 

151.6 

181.9 

212.3 

242.6 

272.9 

45  

30.44 

60.9 

91.3 

121.8 

152.2 

182.6 

213.1 

243.5 

273.9 

50 

30.55 

61.1 

91.7 

122.2 

152.8 

183.3 

213.9 

244.4 

275.0 

55 

30.67 

61.3 

92.0 

122.7 

153.3 

184.0 

214.7 

245.4 

276.0 

60  

30.78 

61.6 

92.3 

123.1 

153.9 

184.7 

215.5 

246.3 

277.0 

Horizontal  dist. 

89.4 

179 

268 

358 

447 

536 

626 

715 

805 

IQo      5' 

i  y  10  

30.90 
31.01 

61.8 
62.0 

92.7 
93.0 

123.6 
124.0 

154.5 
155.1 

185.4 
186.1 

216.3 
217.1 

247.2 
248.1 

278.1 
279.1 

15  

31.12 

62.3 

93.4 

124.5 

155.6 

186.8 

217.9 

249.0 

280.1 

20  

31.24 

62.5 

93.7 

125.0 

156.2 

187.4 

218.7 

249.9 

281.2 

25  ...... 

31.35 

62.7 

94.1 

125.4 

156.8 

188.1 

219  .  5 

250.8 

282.2 

30  

31.47 

62.9 

94.4 

125.9 

157.3 

188.8 

220.3 

251.7 

283.2 

35  

31.58 

63.2 

94.7 

126.3 

157.9 

189.5 

221.1 

252.6 

284.2 

40  

31.69 

63.4 

95.1 

126.8 

158.5 

190.1 

221.8 

253.5 

285.2 

45  

31.80 

63.6 

95.4 

127.2 

159.0 

190.8 

222.6 

254.4 

286.2 

50  

31.92 

63.8 

95.7 

127.7 

159.6 

191.5 

223.4 

255.3 

287.2 

55  

32.03 

64.1 

96.1 

128.1 

160.1 

192.2 

224.2 

256.2 

288.3 

60  

32.14 

64.3 

96.4 

128.6 

160.7 

192.8 

225.0 

257.1 

289.3 

Horizontal  dist. 

88.3 

177 

265 

353 

442 

530 

618 

706 

795 

MISCELLANEOUS   TABLES   AND  DATA 
TABLE   58.— TRIGONOMETRIC   FORMULAE 


SOLUTION  OF  OBLIQUE  TRIANGLES. 
B 


273 


A,  B,a 


A,a,b 


C,  a,  6 


FORMULA. 


C\b,c 


,  C,  c 


a,  6,  c 


in 

li 

12  j  A,  B,  C,  a 


16  (A  -B) 
A,B 


C  =180<>- (4  + B),         &  =  ^Z 

C=iinVh^  +  *) 
sin  B  =  — ^  .  &,  C  =  180°  - 


.sin£. 


sin 


.  sin  C. 


•=<-+»>Sg»-« 


sin  y2(A  -  B) 


vers  ^4. 


JC  =  ¥»  (s  -a)  (s-  b)  (s  -  c) 

7T—  a— ^inL^-Lsin_? 

"*  "        2  Bin  ^4" 


Table  58  is  reproduced  by  permission  from  "  Field  Engineering,"  by  Wm.  H.  Searles. 


274  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

TABLE  58  (Continued).— TRIGONOMETRIC  FORMULAE 


GENERAL  FORMULAE. 

13 

sin  A    = 

.     =     VI  —  cos8  A    =    tan  A  cos  A 
cosec  A 

14 
15 

sin  A    = 
sin  A    = 

2  sin  y±  A  cos  J-j  A    =    vers  A  cot  J£  .4 

Y  14  vers  2  ^4    =      4/^£  (1  —  cos  2  A) 

16 

cos  A    = 

-  —  —  r    =     V  '  1  —  sin2  ^4    =    cot  .4  sin  .4 
sec  -  1 

17 
18 
19 

20 

cos  A    = 

cos  A    = 

tan  A    = 

tan  A    = 

1  —  vers  .4    =     2  cos2  \^A  —  1    =    1  —  2  sin2  Jfc  A 

cos8  y*A  —  sin3  J4--1     =    y  %  -{-}<icos2  A 
1               sin  ^4 

/I                            VI  —  cos2  ^4               sin  2  ^4. 

y   cos3  A                            cos  -4                  1  +  cos  2  4 

21 
22 

tan  A    = 

cot  A    = 

1  —  cos  2  ^4    _    vers  2  A    _              % 
1                  rns    4 

_     COS  ul              vVo«w>P2^4       1 

tan.4          sin^l    B 

23 

cot  A    = 

sin  2  ^4                 sin  2  ^4             1  +  0082^ 
1  —  cos  2  ^4    =       vers  2  .4                sin  2  ^4 

24 

cot  A    = 

tanj^.4 
exsec  A 

25 

vers  A    •• 

=    1  —  cos  ^4    =    sin  A  tan  $£A    =    2  sin2  ^  -4 

26 

vers  A 

=    exsec  A  cos  ^4 

27 

exsec  A 

=    sec  A  —  \    =    tan  A  tan  }4A    =    -^  Q1^- 

28 
29 

30 
31 

sin  *4  A 
sin  2^4 
cos  ^A 
cos  2  A 

/l  —  cos  A               /  vers  A 

=    2  sin  ^4  cos  A 

/I  +  cos  A 

=    2  cos2  ^4  —  1    =     cos*  A  —  sin'"  A    =     1  —  2  sin*  A 

MISCELLANEOUS   TABLES  AND  DATA  275 

TABLE  58  (Concluded).— TRIGONOMETRIC  FORMULAE 

GENERAL  FORMULA. 


32  tan  M  A  =  *-£=  ~-r  =  cosec  A  —  cot  A 


Sin  A          1  +  COSJ. 
——-- 


2+ 

37   vers  2  A  =2  sin*  A  =2  sin  A  coa  A  tan 
1  -cos  A 


38  exsec  ^  A  = 


(1  +cos  A)  +  V 


40  sin  (^d  ±  B)  =  sin  ^  .  cos  B  ±  sin  B  .  cos  ^L 

41  cos  (A±B)  —  cos  ^4  .  cos  B  T  sin  ^4  .  sin  B 

42  sin  A  +  sin  B  =  2  sin  J$  (4  -f  B)  cos  ^(A  —  B) 

43  sin  ^  —  sin  5  =  2  cos  f6  (4  +  B)  sin  J^  (^1  —  B) 

44  cos  w4  +  cos  B  =  2  cos  yz  (A  +  B)  cos  ^(A      B) 

45  cos  £  —  cos  A  =  2  sin  ^  (4  -f  5)  sin  }£  (4  —  B) 

46  sin2  .4  —  sin»  5  =  cos3  5  —  cos2  A  =  sin  (4  +  B)  sin  (^  —  B) 

47  cos2  ^  —  sin2  B  =  cos  (^4  -f  B)  cos  04  —  B) 


-- 

cos  ^L  .  cos  B 


- 
cos  -4  .  cos  B 


276 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


D  =  Degree  of  curve. 
L  =  Length  of  curve. 
C= Length  of  long  chord  =  A  B. 


MISCELLANEOUS  TABLES  AND  DATA 
TABLE   59. — CURVE   FORMULA 


277 


GIVEN. 

SOUGHT. 

FORMULAE. 

1 

D 

* 

50 

~  sin^D 

2 

R 

D 

8in«J>=-§- 

3 

A,  D 

L 

£=»»-£. 

4 

A« 

A 

A   ~-PL— 

5 

»,i 

z> 

z>  =  ioo-A_ 

6 

B,    A 

r 

T  =  #  tan  l£  A 

7 

" 

c 

C  =  2  R  sin  ^  A 

8 
9 

: 

M 

E 

If  =  R  vers  ^  A 
E  —  R  exsec  J^  A 

10 

T,    A 

R 

J2=  Tcot^  A 

11 
12 

M 

E 
C 

^7=  Ttan  14  A 
C  =  2  T  cos  J^  A 

13 

H 

M 

Jlf  =  T  cot  J^  A  .  vers  JjjJ  A 

14 

E,    A 

R 

J2-           ^ 

exsec  Jij  A 

15 

" 

T 

T=  E  cot  }4  A 

16 

« 

C 

_,          j.,     sin  ^  A 
exsec  J£  A 

17 

M 

M 

Jf  =  .E7COS  J^  A 

18 

C,    A 

R 

12-           C 

2  sin  J£  A 

19 

20 

H 

M 
T 

lf»Moa»M* 

T          2  COS  ^  A 

21 

22 
23 
24 

25 

M 

If,    A 

ct 

E 

R 
C 
T 

E 

T?  — 

vers  %  A 
C  =  2  3f  cot  ^  A 
tan^A 

M  vers  ^  A 

~~    COS  %  A 

Table  59  is  reproduced  by  permission  from  "  Field  Engineering,"  by  Wm.  H.  Searles. 


278  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

TABLE  59  (Continued) .—CURVE  FORMULA 


GIVEN. 

SOUGHT. 

FORMULA. 

26 
27 

28 
29 

R,   T 

R,  C 
«t 

A 
A 

tan  ^  A  =  -~ 
T 

COS^A    =     ^.|/  (*  +  £)(*-£) 

30 

R,  M 

A 

M 

vers  J^  A  =  -=j- 

31 
32 

R,  E 

A 

R-M 

E 
exsec  ^3  A  =  —  p- 

33 

« 

« 

COS^A=-^— 

34 

35 

t 

r,  c 

A 

C 

COS  K  A    =  — 

tan  W  A  =  A  /  %  T  —  G 
V  2T+C 

36 
37 
38 
39 

T,  E 
C,  M 

A 

A 

tan  J4  A  =  -r- 

cos  J^  A  —  m  a   i    EI  a 

cos  J^  A  =  Ca-^4  jf  a 

40 

M,  E 

A 

3f 

COS  ^  A    =  —  =- 

41 
42 
43 
44 
45 

46 
47 

R,  T 

M 

R,  C 

M 

C 

M 

E 
T 

M 
E 

tan  J4  A  =  A/  _E  ~__ 

ilf      JB 

yra+^2 

E=   VT*  +  R*-R 

2j/(^+l)(^-|) 

722 

=  tfTB  +  HcTTR—KC) 

MISCELLANEOUS   TABLES   AND   DATA 
TABLE  59  (Conceded).— CURVE   FORMULAE 


279 


P.,   II 


A  E 


T,  C 


T,  E 


C,M 


.If, 


T,  M 


C,  E 


T 
C 

E 
T 
C 

M 
R 

M 

JS 

X 

c 

M 

P. 
T 
X 

T 
C 


E 
C 

R 

T 
M 


R-M 


C  =    2VM(2R  -M) 


T  = 


C  = 


2R 


M- 


CT 


2T+C 
(T+E}(T-E) 


2M 


rp  


2  ((72  _  4  If2) 


280 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  60 


Common  Logarithms 


no     123456789 

10 

ooooo 

00432 

00860 

01284 

01703 

02119 

02531 

02938 

03342 

03743 

ii 

04139 

04532 

04922 

05308 

05690 

06070 

06446 

06819 

07188 

07555 

12 

07918 

08279 

08636 

08991 

09342 

09691 

10037 

10380 

10721 

11059 

13 

"394 

11727 

12057 

12385 

12710 

J3033 

13354 

13672 

13988 

14301 

14 

14613 

14922 

15229 

15534 

15836 

16137 

i6435 

16732 

17026 

i73J9 

IS 

17609 

17898 

18184 

18469 

18752 

19033 

19312 

19590 

19866 

20140 

16 

20412 

20683. 

20952 

21219 

21484 

21748 

22OII 

22272 

22531 

22789 

17 

23045 

23300 

23553 

23805 

24055 

24304 

24551 

24797 

25042 

25285 

18 

25527 

25768 

26007 

26245 

26482 

26717 

26951 

27184 

27416 

27646 

19 

27875 

28103 

28330 

28556 

28780 

29003 

29226 

29447 

29667 

29885 

20 

30103 

30320 

30535 

30750 

30963 

3H75 

31387 

31597 

31806 

32015 

21 

32222 

32428 

32634 

32838 

33041 

33244 

33445 

33646 

33846 

34044 

22 

34242 

34439 

34635 

34830 

35025 

352i8 

354II 

35603 

35793 

35984 

23 

36i73 

36361 

36549 

36736 

36922 

37io7 

37291 

37475 

37658 

37840 

24 

38021 

38202 

38382 

38561 

38739 

38917 

39094 

39270 

39445 

39620 

25 

39794 

39967 

40140 

40312 

40483 

40654 

40824 

40993 

41162 

41330 

26 

4M97 

41664 

41830 

41996 

42160 

42325 

42488 

42651 

42813 

42975 

27 

43136 

43297 

43457 

43616 

43775 

43933 

44091 

44248 

44404 

4456o 

28 

44716 

44871 

45025 

45179 

45332 

45484 

45637 

45788 

45939 

46090 

29 

46240 

46389 

46538 

46687 

46835 

46982 

47129 

47276 

47422 

47567 

30 

47712 

47857 

48001 

48144 

48287 

48430 

48572 

48714 

48855 

48996 

31 

49136 

49276 

49415 

49554 

49693 

49831 

49969 

50106 

50243 

50379 

32 

50515 

50651 

50786 

50920 

5^55 

51188 

51322 

5M55 

51587 

51720 

33 

5i85i 

51983 

52114 

52244 

52375 

52504 

52634 

52763 

52892 

53020 

34 

53148 

53275 

53403 

53529 

53656 

53782 

53908 

54033 

54158 

54283 

35 

54407 

54531 

54654 

54777 

54900 

55023 

55U5 

55267 

55388 

55509 

36 

55630 

55751 

55871 

5599i 

56110 

56229 

56348 

56467 

56585 

56703 

37 

56820 

56937 

57054 

57i7i 

57287 

57403 

57519 

57634 

57749 

57864 

38 

57978 

58092 

58206 

58320 

58433 

58546 

58659 

58771 

58883 

58995 

39 

59106 

592I8 

59329 

59439 

59550 

5966o 

59770 

59879 

59988 

60097 

40 

60206 

60314 

60423 

60531 

60638 

60746 

60853 

60959 

61066 

61172 

41 

61278 

61384 

61490 

6i595 

61700 

61805 

61909 

62014 

62118 

62221 

42 

62325 

62428 

62531 

62634 

62737 

62839 

62941 

63043 

63144 

63246 

43 

63347 

63448 

63^48 

63649 

63749 

63849 

63949 

64048 

64147 

64246 

44 

64345 

64444 

64542 

64640 

64738 

64836 

64933 

65031 

65128 

65225 

45 

65321 

65418 

65514 

65610 

65706 

65801 

65896 

65992 

66087 

66181 

46 

66276 

66370 

66464 

66558 

66652 

66745 

66839 

66932 

67025 

67117 

47 

67210 

67302 

67394 

67486 

67578 

67669 

67761 

67852 

67943 

68034 

48 

68124 

68215 

68305 

68395 

68485 

68574 

68664 

68753 

68842 

68931 

49 

69020 

69108 

69197 

69285 

69373 

69461 

69548 

69636 

69723 

69810 

So 

69897 

69984 

70070 

7oi57 

70243 

70329 

70415 

70501 

70586 

70672 

51 

70757 

70842 

70927 

71012 

71096 

71181 

71265 

71349 

71433 

7i5i7 

52 

71600 

71684 

71767 

71850 

71933 

72016 

72099 

72181 

72263 

72346 

53 

72428 

72509 

72591 

72673 

72754 

72835 

72916 

72997 

73078 

73159 

54 

73239 

73320 

73400 

7348o 

7356o 

73640 

73719 

73799 

73878 

73957 

0123456789 

Table  60  is  reproduced  by  permission  from  "  American  Civil  Engineers'  Pocket  Book, 
Mansfield  Merriman,  Editor-in-Chief. 


MISCELLANEOUS   TABLES  AND  DATA 


281 


of  Numbers  from  000  to  999 


n     o     i     2     34     56789 

55 

74036 

74H5 

74194 

74273 

74351 

74429 

74507 

74586 

74663 

74741 

56 

748i9 

74896 

74974 

75051 

75128 

75205 

75282 

75358 

75435 

755H 

57 

75587 

75664 

75740 

758i5 

75891 

75967 

76042 

76118 

76193 

76268 

58 

76343 

76418 

76492 

76567 

76641 

76716 

76790 

76864 

76938 

77012 

59 

77085 

77*59 

77232 

77305 

77379 

77452 

77525 

77597 

77670 

77743 

60 

778.15 

77887 

77960 

78032 

78104 

78176 

78247 

78319 

78390 

78462 

61 

78533 

78604 

78675 

78746 

78817 

78888 

78958 

79029 

79099 

79169 

62 

79239 

79309 

79379 

79449 

795i8 

79588 

79657 

79727 

79796 

79865 

63 

79934 

80003 

80072 

80140 

80209 

80277 

80346 

80414 

80482 

80550 

64 

80618 

80686 

80754 

80821 

80889 

80956 

81023 

81090 

81158 

81224 

65 

81291 

81358 

81425 

81491 

81558 

81624 

81690 

8i757 

81823 

81889 

66 

8i954 

82020 

82086 

82151 

82217 

82282 

82347 

82413 

82478 

82543 

67 

82607 

82672 

82737 

82802 

82866 

82930 

82995 

83059 

83123 

83187 

68 

83251 

83315 

83378 

83442 

83506 

83569 

83632 

83696 

83759 

83822 

69 

83885 

83948 

84011 

84073 

84136 

84198 

84261 

84323 

84386 

84448 

70 

84510 

84572 

84634 

84696 

84757 

84819 

84880 

84942 

85003 

85065 

7i 

85126 

85187 

85248 

85309 

85370 

85431 

85491 

85552 

85612 

85673 

72 

85733 

85794 

85854 

85914 

85974 

86034 

86094 

86153 

86213 

86273 

73 

86332 

86392 

86451 

86510 

86570 

86629 

86688 

86747 

86806 

86864 

74 

86923 

86982 

87040 

87099 

87157 

87216 

87274 

87332 

87390 

87448 

75 

87506 

87564 

87622 

87679 

87737 

87795 

87852 

87910 

87967 

88024 

76 

88081 

88138 

88195 

88252 

88309 

88366 

88423 

88480 

88536 

88593 

77 

88649 

88705 

88762 

88818 

88874 

88930 

88986 

89042 

89098 

89154 

78 

89209 

89265 

89321 

89376 

89432 

89487 

89542 

89597 

89653 

89708 

79 

89763 

89818 

89873 

89927 

89982 

90037 

90091 

90146 

90200 

90255 

80 

90309 

90363 

90417 

90472 

90526 

90580 

90634 

90687 

90741 

90795 

81 

90849 

90902 

90956 

91009 

91062 

91116 

91169 

91222 

91275 

91328 

82 

91381 

9*434 

91487 

91540 

91593 

91645 

91698 

9i75i 

91803 

91855 

83 

91908 

91960 

92012 

92065 

92117 

92169 

92221 

92273 

92324 

92376 

84 

92428 

92480 

92531 

92583 

92634 

92686 

92737 

92788 

92840 

92891 

85 

92942 

92993 

93044 

93095 

93146 

93197 

93247 

93298 

93349 

93399 

86 

93450 

935oo 

93551 

936oi 

93651 

93702 

93752 

93802 

93852 

93902 

87 

93952 

94002 

94052 

94IOI 

94i5i 

94201 

94250 

943oo 

94349 

94399 

88 

94448 

94498 

94547 

94596 

94645 

94694 

94743 

94792 

94841 

94890 

89 

94939 

94988 

95036 

95085 

95134 

95182 

95231 

95279 

95328 

95376 

90 

95424 

95472 

95521 

95569 

95617 

95665 

95713 

9576i 

95809 

95856 

9i 

95904 

95952 

95999 

96047 

96095 

96142 

96190 

96237 

96284 

96332 

92 

96379 

96426 

96473 

96520 

96567 

96614 

96661 

96708 

96755 

96802 

93 

96848 

96895 

96942 

96988 

97035 

97081 

97128 

97174 

97220 

97267 

94 

97313 

97359 

97405 

97451 

97497 

97543 

97589 

97635 

97681 

97727 

95 

97772 

97818 

97864 

97909 

97955 

98000 

98046 

98091 

98i37 

98182 

96 

98227 

98272 

98318 

98363 

98408 

98453 

98498 

98543 

98588 

98632 

97 

98677 

98722 

98767 

98811 

98856 

98900 

98945 

98989 

99034 

99078 

98 

99123 

99167 

99211 

99255 

99300 

99344 

99388 

99432 

99476 

99520 

99 

99564 

99607 

99651 

99695 

99739 

99782 

99826 

99870 

99913 

99957 

01     23     4     56     789 

282 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  61 
SINE 


Natural  Sines 


Angle   o'     10'     20'    30'     40'    50'     60' 

0° 

o.ooooo 

0.00291 

0.00582 

0.00873 

0.01164 

0.01454 

0.01745 

89 

z 

0.01745 

0.02036 

0.02327 

0.02618 

0.02908 

0.03199 

0.03490 

88 

2 

0.03490 

0.03781 

0.04071 

0.04362 

0.04653 

0.04943 

0.05234 

87 

3 

0.05234 

0.05524 

0.05814 

0.06105 

0.06395 

0.06685 

0.06976 

86 

4 

0.06976 

0.07266 

0.07556 

0.07846 

0.08136 

0.08426 

0.08716 

85° 

5° 

0.08716 

0.09005 

0.09295 

0.09585 

0.09874 

0.10164 

0.10453 

84 

6 

0.10453 

o.  10742 

0.11031 

0.11320 

o.  11609 

0.11898 

0.12187 

83 

7 

0.12187 

0.12476 

0.12764 

0.13053 

0.13341 

0.13629 

0.13917 

82 

8 

0.13917 

0.14205 

o.i4493 

0.14781 

0.15069 

0.15356 

0.15643 

81 

9 

0.15643 

Q.I5931 

0.16218 

0.16505 

0.16792 

0.17078 

0.17365 

80° 

10° 

0.17365 

0.17651 

0.17937 

0.18224 

0.18509 

0.18795 

o.  19081 

79 

ii 

o.  19081 

0.19366 

0.19652 

0.19937 

O.  2O222 

0.20507 

o.  20791 

78 

12 

0.20791 

0.21076 

0.21360 

0.21644 

0.21928 

O.  22212 

0.22495 

77 

13 

0.22495 

0.22778 

0.23062 

0.23345 

0.23627 

0.23910 

0.24192 

76 

14 

0.24192 

0.24474 

0.24756 

0.25038 

0.25320 

o.  25601 

0.25882 

75° 

15° 

0.25882 

0.26163 

0.26443 

o.  26724 

0.27004 

o.  27284 

0.27564 

74 

16 

0.27564 

0.27843 

0.28123 

0.28402 

0.28680 

0.28959 

0.29237 

73 

17 

0.29237 

0.29515 

0.29793 

0.30071 

0.30348 

0.30625 

0.30902 

73 

18 

0.30902 

0.31178 

0.31454 

0.31730 

0.32006 

0.32282 

0.32557 

71 

19 

o.32557 

0.32832 

0.33106 

0.33381 

0.33655 

0.33929 

0.34202 

70° 

20° 

0.34202 

0-34475 

0.34748 

0.35021 

0.35293 

0.35565 

0.35837 

69 

21 

0.35837 

0.36108 

0.36379 

0.36650 

0.36921 

0.37191 

0.37461 

68 

22 

0.37461 

o.3773o 

0.37999 

0.38268 

0.38537 

0.38805 

0.39073 

67 

23 

0.39073 

o.3934i 

0.39608 

0.39875 

O.4OI42 

o  .  40408 

0.40674 

66 

24 

0.40674 

0.40939 

0.41204 

0.41469 

0.41734 

0.41998 

0.42262 

65° 

as° 

0.42262 

0.42525 

0.42788 

0.43051 

0.43313 

0.43575 

0.43837 

64 

26 

0.43837 

0.44098 

0.44359 

0.44620 

0.44880 

0.45140 

0.45399 

63 

27 

0.45399 

0.45658 

0.45917 

0.46175 

0.46433 

0.46690 

0.46947 

62 

28 

0.46947 

0.47204 

0.47460 

0.47716 

0.47971 

0.48226 

0.48481 

61 

29 

0.48481 

0.48735 

0.48989 

0.49242 

0.49495 

0.49748 

0.50000 

60° 

30° 

0.50000 

0.50252 

0.50503 

0.50754 

0.51004 

0.51254 

0.51504 

59 

31 

0.51504 

o.5r753 

o.  52002 

0.52250 

o.  52498 

0.52745 

0.52992 

58 

32 

0.52992 

0.53238 

0.53484 

o.5373o 

0.53975 

0.54220 

0.54464 

57 

33 

0.54464 

0.54708 

o.5495i 

o.55i94 

0.55436 

0.55678 

0.55919 

56 

34 

0.559^ 

0.56160 

0.56401 

0.56641 

0.56880 

0.57119 

0.57358 

55° 

35° 

0.57358 

0.57596 

0.57833 

0.58070 

0.58307 

0.58543 

0.58779 

54 

36 

0.58779 

0.59014 

0.59248 

0.59482 

0.59716 

0.59949 

0.60182 

53 

37 

0.60182 

0.60414 

0.60645 

0.60876 

0.61107 

0.61337 

0.61566 

52 

38 

0.61566 

0.61795 

0.62024 

0.62251 

0.62479 

0.62706 

0.62932 

Si 

39 

0.62932 

0.63158 

0.63383 

0.63608 

0.63832 

0.64056 

0.64279 

50° 

40° 

0.64279 

0.64501 

0.64723 

0.64945 

0.65166 

0.65386 

0.65606 

49 

41 

0.65606 

0.65825 

0.66044 

0.66262 

0.66480 

0.66697 

0.66913 

48 

42 

0.66913 

0.67129 

0.67344 

0.67559 

0.67773 

0.67987 

0.68200 

47 

43 

0.68200 

0.68412 

0.68624 

0.68835 

0.69046 

0.69256 

0.69466 

46 

44 

0.69466 

0.69675 

0.69883 

o.  70091 

0.70298 

0.70505)0,70711 

45 

60'    50'     40'     30'      20'     xo'      o'  Angle 

COSINE 

Table  61  is  reproduced  by  permission  from  "  American  Civil  Engineers'  Pocket  Book, 
Mansfield  Merriman,  Editor-in-Chief. 


MISCELLANEOUS   TABLES  AND  DATA 


283 


and  Cosines 


SINE 


Angl 

e    o' 

TO' 

20' 

30' 

40' 

50' 

60' 

45? 

0.70711 

0.70916 

0.71121 

0.71325 

0.71529 

0.71732 

0.71934 

44 

46 

o-7I934 

0.72136 

0.72337 

0.72537 

0.72737 

0.72937 

0.73135 

43 

47 

0.73135 

0-73333 

0.73531 

0.73728 

0.73924 

0.74120 

0.74314 

42 

48 

0.74314 

0.74509 

0.74703 

0.74896 

0.75088 

0.75280 

0.75471 

41 

49 

0-7S471 

0.75661 

0.75851 

o.  76041 

0.76229 

0.76417 

0.76604 

40° 

50° 

0.76604 

0.76791 

0.76977 

0.77162 

0-77347 

0-77531 

0.77715 

39 

51 

0.77715 

0.77897 

0.78079 

0.78261 

0.78442 

0.78622 

0.78801 

38 

52 

0.78801 

0.78980 

0.79158 

0.79335 

0.79512 

o.  79688 

0.79864 

37 

53 

o.  79864 

0.80038 

0.80212 

0.80386 

0.80558 

0.80730 

0.80902 

36 

54 

0.80902 

0.81072 

0.81242 

0.81412 

0.81580 

0.81748 

0.81915 

35° 

55° 

0.81915 

0.82082 

0.82248 

0.82413 

0.82577 

0.82741 

0.82904 

34 

56 

0.82904 

0.83066 

0.83228 

0.83389 

0.83549 

0.83708 

0.83867 

33 

57 

0.83867 

0.84025 

0.84182 

0.84339 

0.84495 

0.84650 

0.84805 

32 

58 

0.84805 

0.84959 

0.85112 

0.85264 

0.85416 

0.85567 

0.85717 

31 

59 

0.85717 

0.85866 

0.86015 

0.86163 

0.86310 

0.86457 

0.86603 

30° 

60° 

0.86603 

0.86748 

0.86892 

0.87036 

0.87178 

0.87321 

0.87462 

29 

61 

0.87462 

0.87603 

0.87743 

0.87882 

0.88020 

0.88158 

0.88295 

28 

62 

0.88295 

0.88431 

0.88566 

0.88701 

0.88835 

0.88968 

0.89101 

27 

63 

0.89101 

0.89232 

0.89363 

0.89493 

0.89623 

0.89752 

0.89879 

26 

64 

0.89879 

0.90007 

0.90133 

0.90259 

0.90383 

0.90507 

0.90631 

25° 

65° 

0.90631 

0.90753 

0.90875 

0.90996 

0.91116 

0.91236 

0.91355 

24 

66 

0.91355 

0.91472 

0.91590 

0.91706 

0.91822 

0.91936 

0.92050 

23 

67 

0.92050 

0.92164 

0.92276 

0.92388 

0.92499 

0.92609 

0.92718 

22 

68 

0.92718 

0.92827 

0.92935 

0.93042 

0.93148 

0.93253 

0.93358 

21 

69 

0-93358 

0.93462 

0.93565 

0.93667 

0.93769 

0.93869 

0.93969 

20° 

70° 

0.93969 

0.94068 

0.94167 

0.94264 

0.94361 

0.94457 

0.94552 

19 

71 

0.94552 

0.94646 

0.94740 

0.94832 

0.94924 

0.95015 

0.95106 

18 

72 

0.95106 

.95195 

0.95284 

0.95372 

0-95459 

0.95545 

0.95630 

17 

73 

0.95630 

•957*5 

0-95799 

0.95882 

0.95964 

0.96046 

0.96126 

16 

74 

0.96126 

.96206 

0.96285 

0.96363 

0.96440 

0.96517 

0.96593 

15° 

75° 

0.96593 

.96667 

0.96742 

0.96815 

0.96887 

0.96959 

0.97030 

14 

76 

0.97030 

.97100 

0.97169 

0.97237 

0.97304 

0.97371 

0.97437 

13 

77 

0-97437 

0.97502 

0.97566 

0.97630 

0.97692 

0-97754 

0.97815 

12 

78 

0.97815 

0.97875 

0.97934 

0.97992 

0.98050 

0.98107 

0.98:63 

ZZ 

79 

0.98163 

0.98218 

0.98272 

0.98325 

0.98378 

0.98430 

0.98481 

Z0° 

80° 

0.98481 

0.98531 

0.98580 

0.98629 

0.98676 

0.98723 

0.98769 

9 

8r 

0.98769 

0.98814 

0.98858 

0.98902 

0.98944 

0.98986 

0.99027 

8 

82 

0.99027 

0.99067 

0.99106 

0.99144 

0.99182 

0.99219 

0.99255 

7 

83 

0.99255 

0.99290 

0.99324 

0.99357 

0.99390 

0.99421 

0.99452 

6 

84 

0.99452 

0.99482 

0.99511 

0.99540 

0.99567 

0-99594 

0.99619 

5° 

85° 

0.99619 

0.99644 

0.99668 

0.99692 

0.99714 

0.99736 

0.99756 

4 

86 

0.99756 

0.99776 

0.99795 

0.99813 

0.99831 

0.99847 

0.99863 

3 

87 

0.99863 

0.99878 

0.99892 

0.99905 

0.99917 

0.99929 

0.99939 

2 

88 

0-99939 

0.99949 

0.99958 

0.99966 

0-99973 

0.99979 

0.99985 

Z 

89 

0.99985 

0.99989 

0.99993 

0.99996 

0.99998 

1  .  00000 

I  .  OOOOO 

0° 

60' 

So' 

40' 

30' 

20' 

10' 

o'  A 

ngle 

COSINE 


284 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE   62 
TANGENT 


Natural  Tangents 


Angl< 

;   o' 

10' 

20' 

30' 

40' 

50' 

60' 

0° 

0.00000 

0.00291 

0.00582 

0.00873 

0.01164 

0.01455 

0.01746 

89 

i 

0.01746 

0.02036 

0.02328 

0.02619 

0.02910 

0.03201 

0.03492 

88 

2 

0.03492 

0.03783 

0.04075 

0.04366 

0.04658 

0.04949 

0.05241 

87 

3 

0.05241 

0.05533 

0.05824 

o.  06116 

.  06408 

0.06700 

0.06993 

86 

4 

0.06993 

0.07285 

0.07578 

0.07870 

.08163 

0.08456 

0.08749 

85° 

5° 

0.08749 

0.09042 

0.09335 

0.09629 

.09923 

o.  10216 

o.  10510 

84 

6 

o.  10510 

o.  10805 

o.  11099 

0.11394 

.11688 

0.11983 

o.  12278 

83 

7 

o.  12278 

0.12574 

0.12869 

0.13165 

.13461 

0.13758 

o.  14054 

82 

8 

0.14054 

O.I4351 

o.  14648 

0.14945 

0.15243 

0.15540 

0.15838 

81 

9 

0.15838 

0.16137 

0.16435 

0.16734 

0.17033 

0.17333 

0.17633 

80° 

10° 

0.17633 

0.17933 

0.18233 

0.18534 

0.18835 

o.  19136 

0.19438 

79 

XI 

0.19438 

0.19740 

0.20042 

0.20345 

0.20648 

o.  20952 

o.  21256 

78 

12 

0.21256 

o.  21560 

0.21864 

o.  22169 

0.22475 

0.22781 

0.23087 

77 

13 

0.23087 

0.23393 

0.23700 

0.24008 

0.24316 

0.24624 

0.24933 

76 

14 

0.24933 

0.25242 

0.25552 

0.25862 

0.26172 

0.26483 

0.26795 

75° 

15° 

0.26795 

0.27107 

0.27419 

0.27732 

0.28046 

0.28360 

0.28675 

74 

16 

0.28675 

0.28990 

0.29305 

0.29621 

0.29938 

0.30255 

0.30573 

73 

17 

0.30573 

0.30891 

0.31210 

0.31530 

0.31850 

0.32171 

0.32492 

72 

18 

0.32492 

0.32814 

o.33I36 

0.33460 

0.33783 

0.34108 

0.34433 

7i 

19 

0.34433 

0.34758 

o.35085 

0.35412 

0.35740 

0.36068 

0.36397 

70° 

20° 

0.36397 

0.36727 

0.37057 

0.37388 

0.37720 

0.38053 

0.38386 

69 

21 

0.38386 

0.38721 

0.39055 

0.39391 

0.39727 

0.40065 

0.40403 

68 

22 

0.40403 

0.40741 

0.41081 

0.41421 

0.41763 

0.42105 

0.42447 

67 

23 

0.42447 

0.42791 

0.43*36 

0.43481 

0.43828 

0.44175 

0.44523 

66 

24 

0.44523 

0.44872 

0.45222 

0.45573 

0.45924 

0.46277 

0.46631 

65° 

25° 

0.46631 

0.46985 

0.47341 

0.47698 

0.48055 

0.48414 

0.48773 

64 

26 

0.48773 

o.49I34 

0.49495 

0.49858 

0.50222 

0.50587 

0.50953 

63 

27 

0.50953 

0.51320 

0.51688 

0.52057 

0.52427 

0.52798 

0.5317! 

62 

28 

0.5317! 

0.53545 

0.53920 

0.54296 

0.54673 

0.55051 

0-55431 

61 

29 

0.55431 

0.55812 

0.56194 

0.56577 

0.56962 

0.57348 

0.57735 

60° 

30° 

0.57735 

0.58124 

0.58513 

0.58905 

0.59297 

0.59691 

0.60086 

59 

31 

0.60086 

0.60483 

0.60881 

0.61280 

o.  61681 

0.62083 

0.62487 

53 

32 

0.62487 

0.62892 

0.63299 

0.63707 

0.64117 

0.64528 

0.64941 

57 

33 

0.64941 

0.65355 

0.65771 

0.66189 

0.66608 

0.67028 

0.67451 

56 

34 

0.67451 

0.67875 

0.68301 

0.68728 

0.69157 

0.69588 

0.70021 

55° 

35° 

0.70021 

0.70455 

0.70891 

0.71329 

0.71769 

0.72211 

0.72654 

54 

36 

0.72654 

0.73100 

0.73547 

0.73996 

0.74447 

0.74900 

0-75355 

53 

37 

0.75355 

0.75812 

0.76272 

0.76733 

0.77196 

0.77661 

0.78129 

52 

38 

0.78129 

0.78598 

0.79070 

0.79544 

0.80020 

0.80498 

0.80978 

51 

39 

0.80978 

0.81461 

0.81946 

0.82434 

0.82923 

0.83415 

0.83910 

50° 

40° 

0.83910 

0.84407 

0.84906 

0.85408 

0.85912 

0.86419 

0.86929 

49 

41 

0.86929 

0.87441 

0.87955 

0.88473 

0.88992 

0.89515 

0.90040 

48 

42 

0.90040 

0.90569 

0.91099 

0.91633 

0.92170 

0.92709 

0.93252 

47 

43 

0.93252 

0.93797 

0.94345 

0.94896 

o.9545r 

0.96008 

0.96569 

46 

44 

0.96569 

0.97133 

0.97700 

0.98270 

0.98843 

0.99420 

I  .  00000 

45° 

60' 

So' 

40' 

30' 

20' 

10' 

o'  / 

ingle 

COTANGENT 

Table  62  is  reproduced  by  permission  from  "  American  Civil  Engineers'  Pocket  Book, 
Mansfield  Merriman,  Editor-in-Chief. 


MISCELLANEOUS   TABLES  AND  DATA 


285 


and  Cotangents 


TANGENT 


Angl 

B     <>' 

10' 

20' 

30' 

40' 

So' 

60' 

45° 

.  00000 

.00583 

.01170 

.01761 

•02355 

.02952 

•03553 

44 

46 

.03553 

.04158 

.04766 

.05378 

.05994 

.06613 

.07237 

43 

47 

.07237 

.07864 

.08496 

.09131 

.09770 

.  10414 

.  11061 

42 

48 

.11061 

."713 

.12369 

.13029 

.13694 

•  14363 

•15037 

41 

49 

.15037 

•IS7IS 

.  16398 

.17085 

.17777 

.  18474 

•I9I75 

40° 

50° 

.1.9175 

.  19882 

•20593 

.21310 

.22031 

.22758 

•  23490 

39 

Si 

.  23490 

.24227 

.24969 

•257I7 

.26471 

.27230 

.27994 

38 

52 

.27994 

.28764 

.29541 

.30323 

.31110 

•3J904 

.32704 

37 

53 

.32704 

•33511 

•34323 

•35I42 

.35968 

.36800 

•37638 

36 

54 

.37638 

.38484 

.39336 

.40195 

.41061 

.41934 

.42815 

35° 

55° 

.42815 

•43703 

.44598 

.45501 

.46411 

.47330 

•48256 

34 

56 

.48256 

.49190 

.50133 

.  51084 

.52043 

.53010 

•53987 

33 

57 

.53987 

.54972 

.55966 

.56969 

.57981 

.59002 

.  60033 

32 

58 

.60033 

.61074 

.62125 

.63185 

.64256 

•65337 

.66428 

31 

59 

.66428 

.67530 

.68643 

.69766 

.  70901 

.  72047 

•73205 

30° 

60° 

.73205 

.  74375 

.75556 

.76749 

•77955 

.79174 

.  80405 

29 

61 

.  80405 

.81649 

.82906 

.84177 

.85462 

.86760 

•88073 

28 

62 

.88073 

.  89400 

.90741 

.92098 

•93470 

.94858 

.96261 

27 

63 

.96261 

.97680 

.99116 

•00569 

.02039 

.03526 

.05030 

26 

64 

.05030 

•06553 

.08094 

.09654 

-11233 

.12832 

2.14451 

25° 

65° 

•I4451 

.  16090 

•17749 

.  19430 

.21132 

.22857 

2.24604 

24 

66 

.  24604 

.26374 

.28167 

.  29984 

.31826 

.33693 

2.35585 

23 

67 

.35585 

.37504 

•  39449 

.41421 

.43422 

•45451 

2.47509 

22 

68 

.47509 

•49597 

.51715 

•  53865 

.  56046 

.58261 

2.60509 

21 

69 

.60509 

.62791 

.65109 

.67462 

•69853 

.72281 

2.74748 

20° 

70° 

.  74748 

.77254 

.  79802 

.82391 

2.85023 

2.87700 

2.90421 

19 

7i 

.90421 

•93189 

.96004 

.98869 

3-01783 

3  •  04749 

3.07768 

18 

72 

3.07768 

3.  10842 

3-I3972 

3-i7I59 

3  .  20406 

3.23714 

3.27085 

17 

73 

3.27085 

3-30521 

3-34023 

3-37594 

3-41236 

3-44951 

3-48741 

16 

74 

3-48741 

3-52609 

3.56557 

3.60588 

3.64705 

3.68909 

3-73205 

15° 

75° 

3-73205 

3-77595 

3.82083 

3.86671 

3-91364 

3.96165 

4.01078 

14 

76 

4.01078 

4.06107 

4.11256 

4.16530 

4.21933 

4.27471 

4.33148 

13 

77 

4.33148 

4.38969 

4.44942 

4.51071 

4.57363 

4.63825 

4.70463 

12 

78 

4.70463 

4.77286 

4.84300 

4.91516 

4.98940 

5.06584 

5-14455 

II 

79 

5.14455 

5.22566 

5-30928 

5-39552 

5-48451 

5.57638 

5.67128 

IOC 

80° 

5.67128 

5.76937 

5.87080 

5.97576 

6  .  08444 

6.19703 

6.31375 

9 

81 

6.31375 

6.43484 

6.56055 

6.69116 

6.82694 

6.96823 

7.H537 

8 

82 

7-II537 

7.26873 

7.42871 

7-59575 

7.77035 

7-95302 

8.14435 

7 

83 

8.14435 

8.34496 

8-55555 

8.77689 

9.00983 

9-25530 

9.5I436 

6 

84 

9.5M36 

9.78817 

10.0780 

10.3854 

10.  7119 

11.0594 

11.4301 

5° 

85° 

11.4301 

11.8262 

12.2505 

12.7062 

13-1969 

13.7267 

14-3007 

4 

86 

14.3007 

14.9244 

15.6048 

16.3499 

I7-I693 

18.0750 

19.0811 

3 

87 

19.0811 

20.  2056 

21.4704 

22.9038 

24.5418 

26.4316 

28.6363 

2 

88 

28.6363 

31.2416 

34.3678 

38.1885 

42.9641 

49-1039 

57.2900 

X 

89 

57.2900 

68.7501 

85.9398 

114.589 

171.885 

343-774 

00 

0° 

60' 

So' 

40' 

30' 

20' 

10' 

o'  A 

ngle 

COTANGENT 


286 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  63 
THREE-HALVES  POWERS  OF  NUMBERS 


No. 

.000 

.001 

.002 

.003 

.004 

.005 

.006 

.007 

.008 

.009 

0.00 

.0000 

.OOU 

.0002 

.0003 

.0004 

.0005 

.0006 

.0007 

.0008 

.0009 

.01 

.0010 

.0012 

.0014 

.0015 

.0017 

.0019 

.0021 

.0022 

.0024 

.0026 

.02 

.0028 

.0030 

.0033 

.0035 

.0038 

.0040 

.0042 

.0045 

.0047 

.0050 

.03 

.0052 

.0055 

.0058 

.0060 

.0063 

.0066 

.0069 

.0072 

.0074 

.0077 

.04 

.0080 

.0083 

.0086 

.0090 

.0093 

.0096 

.0099 

.0102 

.0106 

.0109 

.05 

.0112 

.0116 

.0119 

.0122 

.0126 

.0130 

.0133 

.0136 

.0140 

.0144 

.06 

.0147 

.0151 

.0155 

.0158 

.0162 

.0166 

.0170 

.0174 

.0177 

.0181 

.07 

.0185 

.0189 

.0193 

.0197 

.0201 

.0206 

.0210 

.0214 

.0218 

.0222 

.08 

.0226 

.0230 

.0235 

.0239 

.0244 

.0248 

.0252 

.0257 

.0261 

.0266 

.09 

.0270 

.0275 

.0279 

.0284 

.0288 

.0293 

.0298 

.0302 

.0307 

.0311 

.10 

.0316 

.0321 

.0326 

.0331 

.0336 

.0340 

.0345 

.0350 

.0355 

.0360 

.11 

.0365 

.0370 

.0375 

.0380 

.0385 

.0390 

.0396 

.0401 

.0406 

.0411 

.12 

.0416 

.0421 

.0427 

.0432 

.0437 

.0442 

.0448 

.0453 

.0458 

.0464 

.13 

.0469 

.0474 

.0480 

.0486 

.0491 

.0496 

.0502 

.0508 

.0513 

.0518 

.14 

.0524 

.0530 

.0535 

.0541 

.0547 

.0552 

.0558 

.0564 

.0570 

.0575 

.15 

.0581 

.0587 

.0593 

.0599 

.0605 

.0610 

.0616 

.0622 

.0628 

.0634 

.16 

.0640 

.0645 

.0652 

.0658 

.0664 

.0670 

.0677 

.0683 

.0689 

.0695 

.17 

.0701 

.0707 

.0714 

.0720 

.0726 

.0732 

.0739 

.0745 

.0751 

.0758 

.18 

.0764 

.0770 

.0777 

.0783 

.0790 

.0796 

.0802 

.0809 

.0815 

.0822 

.19 

.0828 

.0835 

.0841 

.0848 

.0854 

.0861 

.0868 

.0874 

.0881 

.0887 

.20 

.0894 

.0901 

,0908 

.0914 

.0921 

.0928 

.0935 

.0942 

.0948 

.0955 

.21 

.0962 

.0969 

.0976 

.0983 

.0990 

.0997 

.1004 

.1011 

.1018 

.1025 

.22 

.1032 

.1039 

.1046 

.1053 

.1060 

.1068 

.1075 

.1082 

.1089 

.1096 

.23 

.1103 

.1110 

.1118 

.1125 

.1132 

.1140 

.1147 

.1154 

.1161 

.1169 

.24 

.1176 

.1183 

.1191 

.1198 

.1251 

.1213 

.1220 

.1228 

.1235 

.1243 

.25 

.1250 

.1258 

.1265 

.1273 

.1280 

.1288 

.1296 

.1303 

.1311 

.1318 

.26 

.1326 

.1334 

.1341 

.1349 

.1357 

.1364 

.1372 

.1380 

.1388 

.1395 

.27 

.1403 

.1411 

.1419 

.1427 

.1435 

.1442 

.1450 

.1458 

.1466 

.1474 

.28 

.1482 

.1490 

.1498 

.1506 

.1514 

.1522 

.1530 

.1538 

.1546 

.1554 

.29 

.1562 

.1570 

.1578 

.1586 

.1594 

.1602 

.1611 

.1619 

.1627 

.1635 

.30 

.1643 

.1651 

.1660 

.1668 

.1676 

.1684 

.1693 

.1701 

.1709 

.1718 

.31 

.1726 

.1734 

.1743 

.1751 

.1760 

.1768 

.1776 

.1785 

.1793 

.1802 

.32 

.1810 

.1819 

.1827 

.1836 

.1844 

.1853 

.1862 

.1870 

.1879 

.1887 

.33 

.1896 

.1905 

.1913 

.1922 

.1931 

.1940 

.1948 

.1957 

.1966 

.1974 

.34 

.1983 

.1992 

.2001 

.2009 

.2018 

.2027 

.2036 

.2045 

.2053 

.2062 

.35 

.2071 

.2080 

.2089 

.2098 

.2107 

.2116 

.2124 

.2133 

.2142 

.2151 

.36 

.2160 

.2169 

.2178 

.2187 

.2196 

.2206 

.2215 

.2224 

.2233 

.2242 

.37 

.2251 

.2260 

.2269 

.2278 

.2287 

.2296 

.2306 

.2315 

.2324 

.2333 

.38 

.2342 

.2351 

.2361 

.2370 

.2380 

.2389 

.2398 

.2408 

.2417 

.2427 

.39 

.2436 

.2445 

.2455 

.2464 

.2474 

.2483 

.2492 

.2502 

.2511 

.2521 

.40 

.2530 

.2540 

.2549 

.2558 

.2568 

.2578 

.2587 

.2596 

.2606 

.2616 

.41 

.2625 

.2635 

.2644 

.2654 

.2664 

.2674 

.2683 

.2693 

.2703 

.2712 

.42 

.2722 

.2732 

.2742 

.2751 

.2761 

.2771 

.2781 

.2791 

.2800 

.2810 

.43 

.2820 

.2830 

.2840 

.2850 

.2860 

.2870 

.2879 

.2889 

.2899 

.2909 

.44 

.2919 

.2929 

.2939 

.2949 

.2959 

.2969 

.2979 

.2989 

.2999 

.3009 

.45 

.3019 

.3029 

.3039 

.3049 

.3059 

.3070 

.3080 

.3090 

.3100 

.3110 

.46 

.3120 

.3130 

.3140 

.3151 

.3161 

.3171 

.3181 

.3191 

.3202 

.3212 

.47 

.3222 

.3232 

.3243 

.3253 

.3263 

.3274 

.3284 

.3294 

.3304 

.3315 

.48 

.3325 

.3336 

.3346 

.3356 

.3367 

.3378 

.3388 

.3398 

.3409 

.3420 

.49 

.3430 

.3441 

.3451 

.3462 

.3472 

.3483 

.3494 

.3504 

.3515 

.3525 

MISCELLANEOUS   TABLES   AND   DATA 


287 


TABLE  63  (Continued) 
THREE-HALVES  POWERS  OF  NUMBERS 


No. 

.000 

.001 

.002 

.003 

.004 

.005 

.006 

.007 

.008 

.009 

0.50 

.3536 

.3547 

.3557 

.3568 

.3578 

.3589 

.3600 

.3610 

.3621 

.3631 

.51 

.3642 

.3653 

.3664 

.3674 

.3685 

.3696 

.3707 

.3718 

.3728 

.3739 

.52 

.3750 

.3761 

.3772 

.3782 

.3793 

.3804 

.3815 

.3826 

.3836 

.3847 

.53 

.3858 

.3869 

.3880 

.3891 

.3902 

.3913 

.3924 

.3935 

.3946 

.3957 

.54 

.3968 

.3979 

.3990 

.4001 

.4012 

.4024 

.4035 

.4046 

.4057 

.4068 

.55 

.4079 

.4090 

.4101 

.4113 

.4124 

.4135 

.4146 

.4157 

.4169 

.4180 

.56 

.4191 

.4202 

.4213 

.4225 

.4236 

.4247 

.4258 

.4269 

.4281 

.4292  j 

.57 

.4303 

.4314 

.4326 

4337 

.4349 

.4360 

.4371 

.4383 

.4394 

.4406 

.58 

.4417 

.4428 

.4440 

.4452 

.4463 

.4474 

.4486 

.4498 

.4509 

.4520 

.59 

.4532 

.4544 

.4555 

.4567 

.4578 

•  .4590 

.4602 

.4613 

.4625 

.4636 

.60 

.4648 

.4660 

.4671 

.4683 

.4694 

.4706 

.4718 

.4729 

.4741 

.4752 

.61 

.4764 

.4776 

.4788 

.4799 

.4811 

.4823 

.4835 

.4847 

.4858 

.4870 

.62 

.4882 

.4894 

.4906 

.4917 

.4929 

.4941 

.4953 

.4965 

.4976 

.4988 

.63 

.5000 

.5012 

.5024 

.5036 

.5048 

.5060 

.5072 

.5084 

.5096 

.5108 

.64 

.5120 

.5132 

.5144 

.5156 

.5168 

.5180 

.5192 

.5204 

.5216 

.5228 

.65 

.5240 

.5252 

.5264 

.5277 

.5289 

.5301 

.5313 

.5325 

.5338 

.5350 

.66 

.5362 

.5374 

.5386 

.5399 

.5411 

.5423 

.5435 

.5447 

.5460 

.5472 

.67 

.5484 

.5496 

.5509 

.5521 

.5533 

.5546 

.5558 

.5570 

.5582 

.5595 

.68 

.5607 

.5620 

.5632 

.5644 

.5657 

.5670 

.5682 

.5694 

.5707 

.5720 

.69 

.5732 

.5744 

.5757 

.5770 

.5782 

.5794 

.5807 

.5820 

.5832 

.5844 

.70 

.5857 

.5870 

.5882 

.5895 

.5907 

.5920 

.5933 

.5945 

.5958 

.5970 

.71 

.5983 

.5996 

.6008 

.6021 

.6033 

.6046 

.6059 

.6071 

.6084 

.6096 

.72 

.6109 

.6122 

.6135 

.6147 

.6160 

.6173 

.6186 

.6199 

.6211 

.6224 

.73 

.6237 

.6250 

.6263 

.6276 

.6289 

.6302 

.6314 

.6327 

.6340 

.6353 

.74 

.6366 

.6379 

.6392 

.6405 

.6418 

.6430 

.6443 

.6456 

.6469 

.6482 

.75 

.6495 

.6508 

.6521 

.6534 

.6547 

.6560 

.6574 

.6587 

.6600 

.6613 

.76 

.6626 

.6639 

.6652 

.6665 

.6678 

.6692 

.6705 

.6718 

.6731 

.6744 

.77 

.6757 

.6770 

.6783 

.6797 

.6810 

.6823 

.6836 

.6849 

.6863 

.6876 

.78 

.6889 

.6902 

.6916 

.6929 

.6942 

.6956 

.6969 

.6982 

.6995 

.7009 

.79 

.7022 

.7035 

.7049 

.7062 

.7075 

.7088 

.7102 

.7115 

.7128 

.7142 

.80 

.7155 

.7168 

.7182 

.7196 

.7209 

.7222 

.7236 

.7250 

.7263 

.7276 

.81 

.7290 

.7304 

.7317 

.7330 

.7344 

.7358 

.7371 

.7384 

.7398 

.7412 

.82 

.7425 

.7439 

.7452 

.7466 

.7480 

.7494 

.7507 

.7521 

.7535 

.7548 

.83 

.7562 

.7576 

.7589 

.7603 

.7617 

.7630 

.7644 

.7658 

.7672 

.7685 

.84 

.7699 

.7713 

.7727 

.7740 

.7754 

.7768 

.7782 

.7796 

.7809 

.7823 

.85 

.7837 

.7851 

.7865 

.7878 

.7892 

.7906 

.7920 

.7934 

.7947 

.7961 

.86 

.7975 

.7989 

.8003 

.8017 

.8031 

.8045 

.8059 

.8073 

.8087 

.8101 

.87 

.8115 

.8129 

.8143 

.8157 

.8171 

.8185 

.8199 

.8213 

.8227 

.8241 

.88 

.8255 

.8269 

.8283 

.8297 

.8311 

.8326 

.8340 

.8354 

.8368 

.8382 

.89 

.8396 

.8410 

.8424 

.8439 

.8453 

.8467 

.8481 

.8495 

.8510 

.8524 

.90 

.8538 

.8552 

.8567 

.8581 

.8595 

.8610 

.8624 

.8638 

.8652 

.8667 

.91 

.8681 

.8695 

.8710 

.8724 

.8738 

.8752 

.8767 

.8781 

.8795 

.8810 

.92 

.8824 

.8838 

.8853 

.8868 

.8882 

.8896 

.8911 

.8926 

.8940 

.8954 

.93 

.8969 

.8984 

.8998 

.9012 

.9027 

.9042 

.9056 

.9070 

.9085 

.9100 

.94 

.9114 

.9128 

.9143 

.9158 

.9172 

.9186 

.9201 

.9216 

.9230 

.9244 

.95 

.9259 

.9274 

.9288 

.9302 

.9317 

.9332 

.9347 

.9362 

.9377 

.9391 

.96 

.9406 

.9421 

.9435 

.9450 

.9465 

.9480 

.9494 

.9509 

.9524 

.9538 

.97 

.9553 

.9568 

.9583 

.9598 

.9613 

.9628 

.9642 

.9657 

.9672 

.9687 

.98 

.9702 

.9717 

.9732 

.9746 

.9761 

.9776 

.9791 

.9806 

.9820 

.9835 

.99 

.9850 

.9865 

.9880 

.9895 

.9910 

.9925 

.9940 

.9955 

.9970 

.9985 

288 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


TABLE  63  (Continued) 
THREE-HALVES  POWERS  OF  NUMBERS 


No. 

.000 

.001 

.002 

.003 

.004 

.005 

.006 

.007 

.008 

.009 

1.00 

1.0000 

1.0015 

1.0030 

.0045 

.0060 

1.0075 

1.0090 

1.0105 

1.0120 

1.0135 

1.01 

1.0150 

1.0165 

1.0180 

.0196 

.0211 

1.0226 

1.0241 

1.0256 

1.0272 

1.0287 

1.02 

1.0302 

1.0317 

1.0332 

.0347 

.0362 

1.0378 

1.0393 

1.0408 

1.0428 

1.0438 

1.03 

1.0453 

1.0468 

1.0484 

.0499 

.0514 

1.0530 

.0545 

1.0560 

1.0575 

1.0591 

1.04 

1.0606 

1.0621 

1.0637 

.0652 

.0667 

1.0682 

.0698 

1.0713 

1.0728 

1.0744 

1.05 

1.0759 

1.0774 

1.0790 

.0805 

.0821 

1.0836 

.0851 

1.0867 

1.0882 

1.0898 

1.06 

1.0913 

1.0928 

1.0944 

1.0960 

.0975 

1.0990 

.1006 

1.1022 

1.1037 

1.1052 

1.07 

1.1068 

1.1084 

1.1099 

1.1115 

.1130 

1.1146 

.1162 

1.1177 

1.1193 

1.1208 

1.08 

1.1224 

.1240 

.1255 

1.1271 

.1286 

1.1302 

.1318 

1.1333 

1.1349 

1.1364 

1.09 

1.1380 

.1396 

.1411 

1.1427 

.1443 

1.1458 

.1474 

1.1490 

1.1506 

1.1521 

1.10 

1.1537 

.1553 

.1569 

1.1584 

.1600 

1.1616 

.1632 

1.1648 

1.1663 

1.1679 

1.11 

1.1695 

.1711 

.1727 

1.1742 

.1758 

1.1774 

.1790 

1.1806 

1.1821 

1.1837 

1.12 

1.1853 

.1869 

.1885 

1.1901 

.1917 

1.1932 

.1948 

1.1964 

1.1980 

1.1996 

1.13 

1.2012 

1.2028 

.2044- 

1.2060 

.2076 

1.2092 

.2108 

1.2124 

1.2140 

1.2156 

1.14 

1.2172 

1.2188 

.2204 

1.2220 

.2236 

1.2252 

.2268 

1.2284 

1.2300 

.2316 

1.15 

1.2332 

1.2348 

.2364 

1.2381 

.2397 

1.2413 

1.2429 

1.2445 

1.2462 

.2478 

1.16 

1.2494 

1.2510 

.2526 

1.2543 

.2559 

1.2575 

1.2591 

1.2607 

1.2624 

.2640 

1.17 

1.2656 

1.2672 

.2688 

1.2705 

.2721 

1.2737 

1.2753 

1  .2769 

1.2786 

.2802 

1.18 

1.2818 

1.2834 

1.2851 

1.2867 

.2883 

1.2900 

1.2916 

1  .2932 

.2948 

.2965 

1.19 

1.2981 

1.2997 

1.3014 

1.3030 

1.3047 

1.3063 

1  .3079 

1  .3096 

.3112 

.3129 

1.20 

1.3145 

1.3162 

1.3178 

1.3194 

1.3211 

1.3228 

1.3244 

1.3260 

.3277 

.3294 

1.21 

1.3310 

.3326 

1.3343 

1.3360 

1.3376 

1.3392 

1.3409 

1.3426 

.3442 

.3458 

1.22 

1.3475 

.3492 

.3508 

1.3525 

1.3541 

1.3558 

1.3575 

1.3591 

.3608 

.3624 

1.23 

1.3641 

.3658 

.3674 

1.3691 

1.3768 

1.3724 

1.3741 

1.3758 

.3775 

.3791 

1.24 

1.3808 

.3825 

.3841 

.3858 

1.3875 

1.3892 

1.3908 

1.3925 

.3942 

.3958 

1.25 

1.3975 

.3992 

.4009 

.4026 

1.4043 

1.4060 

1.4076 

1.4093 

.4110 

.4127 

1.26 

1.4144 

.4161 

.4178 

.4194 

1.4211 

1.4228 

1.4245 

1.4262 

.4278 

.4295 

1.27 

1.4312 

.4329 

.4346 

.4363 

1.4380 

1.4397 

1.4414 

1.4431 

.4448 

.4465 

1.28 

1.4482 

.4499 

.4516 

.4533 

1.4550 

1.4567 

1.4584 

1.4601 

.4618 

.4635 

1.29 

.4652 

.4669 

.4686 

.4703 

1.4720 

1.4737 

1.4754 

1.4771 

.4788 

.4805 

1.30 

.4822 

.4839 

.4856 

.4874 

1.4891 

1.4908 

1.4925 

1.4942 

.4960 

.4977 

1.31 

.4994 

.5011 

.5028 

.5046 

1.5063 

1.5080 

1.5097 

1.5114 

.5132 

.5149 

1.32 

.5166 

.5183 

.5200 

.5218 

1.5235 

1.5252 

1.5269 

1.5286 

.5304 

.5321 

1.33 

.5338 

.5355 

.5373 

.5390 

1.5408 

1.5425 

1.5442 

1.5460 

.5477 

.5495 

1.34 

.5512 

.5529 

.5547 

.5564 

1.5582 

1.5599 

1.5616 

1.5634 

.5651 

.5669 

1.35 

.5686 

.5703 

.5721 

.5738 

1.5756 

1.5773 

1.5790 

1.5808 

1.5825 

1.5843 

1.36 

.5860 

.5878 

.5895 

.5912 

1.5930 

1.5948 

1.5965 

1.5982 

1.6000 

1.6018 

1.37 

.6035 

.6053 

.6070 

.6088 

1.6105 

1.6123 

1.6141 

1.6158 

1.6176 

1.6193 

1.38 

.6211 

.6229 

.6246 

.6264 

1.6282 

1.6300 

1.6317 

1.6335 

1.6353 

1.6370 

1.39 

.6388 

.6406 

.6423 

.6441 

1.6459 

1.6476 

1.6494 

1.6512 

1.6530 

1.6547 

1.40 

1.6565 

.6583 

.6601 

.6618 

1.6636 

1.6654 

1.6672 

1.6690 

1.6708 

1.6725 

1.41 

1.6743 

.6761 

.6779 

.6796 

1.6814 

1.6832 

1.6850 

1.6868 

1.6885 

.6903 

1.42 

1.6921 

1.6939 

.6957 

.6975 

1.6993 

1.7010 

1.7028 

1.7046 

1.7064 

.7082 

1.43 

1.7100 

1.7118 

.7136 

.7154 

1.7172 

1.7190 

1.7208 

1.7226 

1.7244 

.7262 

1.44 

1.7280 

1.7298 

.7316 

.7334 

1.7352 

1.7370 

1.7388 

1.7406 

1.7424 

.7442 

1.45 

1.7460 

1.7478 

.7496 

1.7514 

1.7532 

1.7550 

1.7569 

1.7587 

1.7605 

.7623 

1.46 

1.7641 

1.7659 

.7677 

1.7696 

1.7714 

1.7732 

1.7750 

1.7768 

1.7787 

.7805 

1.47 

1.7823 

1.7841 

.7859 

1.7878 

1.7896 

1.7914 

1.7932 

1.7950 

1.7969 

.7987 

1.48 

1.8005 

1.8023 

.8042 

1.8060 

1.8078 

1.8096 

1.8115 

1.8133 

1.8151 

.8170 

1.49 

1.8188 

1.8206 

.8225 

1.8243 

1.8261 

1.8280 

1.8298 

1.8316 

1.8334 

1.8353 

MISCELLANEOUS   TABLES   AND   DATA 


289 


TABLE  63  (Continued) 
THREE-HALVES  POWERS  OF  NUMBERS 


No. 

.00 

01 

.02 

.03 

.04 

.05 

.06 

.07 

.08 

.09 

1.5 

1.838 

1.856 

1.874 

1.892 

1.911 

1.930 

1.948 

1.967 

1.986 

2.005 

1.6 

2.024 

2.043 

2.062 

2.081 

2.100 

2.120 

2.139 

2.158 

2.178 

2.197 

1.7 

2.216 

2.236 

2.256 

2.276 

2.295 

2.315 

2.335 

2.355 

2.375 

2.395 

1.8 

2.415 

2.435 

2.455 

2.476 

2.496 

2.516 

2.537 

2.557 

2.578 

2.598 

1.9 

2.619 

2.640 

2.660 

2.681 

2.702 

2.723 

2.744 

2.765 

2.786 

2.807 

2.0 

2.828 

2.850 

2.871 

2.892 

2.914 

2.935 

2.957 

2.978 

3.000 

3.022 

2.1 

3.043 

3.065 

3.087 

3.109 

3.131 

3.152 

3.174 

3.197 

3.219 

3.241 

2.2 

3.263 

3.285 

3.308 

3.330 

3.352 

3.375 

3.398 

3.420 

3.443 

3.465 

2.3 

3.488 

3.511 

3.534 

3.557 

3.580 

3.602 

3.626 

3.649 

3.672 

3.695 

2.4 

3.718 

3.741 

3.765 

3.788 

3.811 

3.835 

3.858 

3.882 

3.906 

3.929 

2.5 

3.953 

3.977 

4.000 

4.024 

4.048 

4.072 

4.096 

4.120 

4.144 

4.168 

2.6 

4.192 

4.217 

4.241 

4.265 

4.290 

4.314 

4.338 

4.363 

4.387 

4.412 

2.7 

4.437 

4.461 

4.486 

4.511 

4.536 

4.560 

4.585 

4.610 

4.635 

4.660 

2.8 

4.685 

4.710 

4.736 

4.761 

4.786 

4.811 

4.837 

4.862 

4.888 

4.913 

2.9 

4.938 

4.964 

4.990 

5.015 

5.041 

5.067 

5.093 

5.118 

5.144 

5.170 

3.0 

5.196 

5.222 

5.248 

5.274 

5.300 

5.327 

5.353 

5.379 

5.405 

5.432 

3.1 

5.458 

5.484 

5.511 

5.538 

5.564 

5.591 

5.617 

5.644 

5.671 

5.698 

3.2 

5.724 

5.751 

5.778 

5.805 

5.832 

5.859 

5.886 

5.913 

5.940 

5.968 

3.3 

5.995 

6.022 

6.049 

6.077 

6.104 

6.132 

6.159 

6.186 

6.214 

6.242 

3.4 

6.269 

6.297 

6.325 

6.352 

6.380 

6.408 

6.436 

6.464 

6.492 

6.520 

3.5 

6.548 

6.576 

6.604 

6.632 

6.660 

6.689 

6.717 

6.745 

6.774 

6.802 

3.6 

6.830 

6.859 

6.888 

6.916 

6.945 

6.973 

7.002 

7.031 

7.060 

7.088 

3.7 

7.117 

7.146 

7.175 

7.204 

7.233 

7.262 

7.291 

7.320 

7.349 

7.378 

3.8 

7.408 

7.437 

7.466 

7.496 

7.525 

7.554 

7.584 

7.613 

7.643 

7.672 

3.9 

7.702 

7.732 

7.770 

7.791 

7.821 

7.850 

7.880 

7.910 

7.940 

7.970 

4.0 

8.000 

8.030 

8.060 

8.090 

8.120 

8.150 

8.181 

8.211 

8:241 

8.272 

4.1 

8.302 

8.332 

8.363 

8.393 

8.424 

8.454 

8.485 

8.515 

8.546 

8.577 

4.2 

8.607 

8.638 

8.669 

8.700 

8.731 

8.762 

8.792 

8.824 

8.854 

8.886 

4.3 

8.917 

8.948 

8.979 

9.010 

9.041 

9.073 

9.104 

9.135 

9.167 

9.198 

4.4 

9.230 

9.261 

9.292 

9.324 

9.356 

9.387 

9.419 

9.451 

9.482 

9.514 

4.5 

9.546 

9.578 

9.610 

9.642 

9.674 

9.706 

9.738 

9.770 

9.802 

9.834 

4.6 

9.866 

9.898 

9.930 

9.963 

9.995 

10.03 

10.06 

10.09 

10.12 

10.16 

4.7 

10.19 

10.22 

10.25 

10.29 

10.32 

10.35 

10.39 

10.42 

10.45 

10.48 

4.8 

10.52 

10.55 

10.58 

10.62 

10.65 

10.68 

10.71 

10.75 

10.78 

10.81 

4.9 

10.85 

10.88 

10.91 

10.95 

10.98 

11.01 

11.05 

11.08 

11.11 

11.15 

5.0 

11.18 

11.21 

11.25 

11.28 

11.31 

11.35 

11.38 

11.42 

11.45 

11.48 

5.1 

11.52 

11.55 

11.59 

11.62 

11.65 

11.69 

11.72 

11.76 

11.79 

11.82 

5.2 

11.86 

11.89 

11.93 

11.96 

11.99 

12.03 

12.06 

12.10 

12.13 

12.17 

5.3 

12.20 

12.24 

12.27 

12.31 

12.34 

12.37 

12.41 

12.44 

12.48 

12.51 

5.4 

12.55 

12.58 

12.62 

12.65 

12.69 

12.72 

12.76 

12.79 

12.83 

12.86 

5.5 

12.90 

12.93 

12.97 

13.00 

13.04 

13.07 

13.11 

13.15 

13.18 

13.22 

5.6 

13.25 

13.29 

13.32 

13.36 

13.39 

13.43 

13.47 

13.50 

13.54 

13.57 

5.7 

13.61 

13.64 

13.68 

13.72 

13.75 

13.79 

13.82 

13.86 

13.90 

13.93 

5.8 

13.97 

14.00 

14.04 

14.08 

14.11 

14.15 

14.19 

14.22 

14.26 

14.29 

5.9 

14.33 

14.37 

14.40 

14.44 

14.48 

14.51 

14.55 

14.59 

14.62 

14.66 

6.0 

14.70 

14.73 

14.77 

14.81 

14.84 

14.88 

14.92 

14.95 

14.99 

15.03 

6.1 

15.07 

15.10 

15.14 

15.18 

15.21 

15.25 

15.29 

15.33 

15.36 

15.40 

6.2 

15.44 

15.48 

15.51 

15.55 

15.59 

15.62 

15.66 

15.70 

15.74 

15.78 

6.3 

15.81 

15.85 

15.89 

15.93 

15.96 

16.00 

16.04 

16.08 

16.12 

16.15 

6.4 

16.19 

16.23 

16.27 

16.30 

16.34 

16.38 

16.42 

16.46 

16.50 

16.53 

290 


WORKING  DATA  FOR  IRRIGATION   ENGINEERS 


TABLE  63  (Concluded) 
THREE-HALVES  POWERS  OF  NUMBERS 


No. 

.00 

.01 

.02 

.03 

.04 

.05 

.06 

.07 

.08 

.09 

6.5 

16.57 

16.61 

16.65 

16.69 

16.72 

16.76 

16.80 

16.84 

16.88 

16.92 

6.6 

16.96 

16.99 

17.03 

17.07 

17.11 

17.15 

17.19 

17.22 

17.26 

17.30 

6.7 

17.34 

17.38 

17.42 

17.46 

17.50 

17.54 

17.58 

17.62 

17.65 

17.69 

6.8 

17.73 

17.77 

17.81 

17.85 

17.89 

17.93 

17.97 

18.01 

18.05 

18.09 

6.9 

18.12 

18.16 

18.20 

18.24 

18.28 

18.32 

18.36 

18.40 

18.44 

18.48 

7.0 

18.52 

18.56 

18.60 

18.64 

18.68 

18.72 

18.76 

18.80 

18.84 

18.88 

7.1 

18.92 

18.96 

19.00 

19.04 

19.08 

19.12 

19.16 

19.20 

19.24 

19.28 

7.2 

19.32 

19.36 

19.40 

19.44 

19.48 

19.52 

19.56 

19.60 

19.64 

19.68 

7.3 

19.72 

19.76 

19.80 

19.85 

19.89 

19.93 

19.97 

20.01 

20.05 

20.09 

7.4 

20.13 

20.17 

20.21 

20.25 

20.29 

20.33 

20.38 

20.42 

20.46 

20.50 

7.5 

20.54 

20.58 

20.62 

20.66 

20.70 

20.75 

20.79 

20.83 

20.87 

20.91 

7.6 

20.95 

20.99 

21.03 

21.08 

21.12 

21.16 

21.20 

21.24 

21.28 

21.32 

7.7 

21.37 

21.41 

21.45 

21.49 

21.53 

21.58 

21.62 

21.66 

21.70 

21.74 

7.8 

21.78 

21.83 

21.87 

21.91 

21.95 

21.99 

22.04 

22.08 

22.12 

22.16 

7.9 

22.20 

22.25 

22.29 

22.33 

22.37 

22.42 

22.46 

22.50 

22.54 

22.58 

8.0 

22.63 

22.67 

22.71 

22.75 

22.80 

22.84 

22.88 

22.93 

22.97 

23.01 

8.1 

23.05 

23.10 

23.14 

23.18 

23.22 

23.27 

23.31 

23.35 

23.40 

23.44 

8.2 

23.48 

23.52 

23.57 

23.61 

23.65 

23.70 

23.74 

23.78 

23.83 

23.87 

8.3 

23.91 

23.96 

24.00 

24.04 

24.09 

24.13 

24.17 

24.22 

24.26 

24.30 

8.4 

24.35 

24.39 

24.43 

24.48 

24.52 

24.56 

24.61 

24.65 

24.69 

24.74 

8.5 

24.78 

24.83 

24.87 

24.91 

24.96 

25.00 

25.04 

25.09 

25.13 

25.18 

8.6 

25.22 

25.26 

25.31 

25.35 

25.40 

25.44 

25.48 

25.53 

25.57 

25.62 

8.7 

25.66 

25.71 

25.75 

25.79 

25.84 

25.88 

25.93 

25.97 

26.02 

26.06 

8.8 

26.10 

26.15 

26.19 

26.24 

26.28 

26.33 

26.37 

26.42 

26.46 

26.51 

8.9 

26.55 

26.60 

26.64 

26.69 

26.73 

26.78 

26.82 

26.87 

26.91 

26.96 

9.0 

27.00 

27.04 

27.09 

27.14 

27.18 

27.23 

27.27 

27.32 

27.36 

27.41 

9.1 

27.45 

27.50 

27.54 

27.59 

27.63 

27.68 

27.72 

27.77 

27.81 

27.86 

9.2 

27.90 

27.95 

28.00 

28.04 

28.09 

28.13 

28.18 

28.22 

28.27 

28.32 

9.3 

28.36 

28.41 

28.45 

28.50 

28.54 

28.59 

28.64 

28.68 

28.73 

28.77 

9.4 

28.82 

28.87 

28.91 

28.96 

29.00 

29.05 

29.10 

29.14 

29.19 

29.23 

9.5 

29.28 

29.33 

29.37 

29.42 

29.47 

29.51 

29.56 

29.61 

29.65 

29.70 

9.6 

29.74 

29.79 

29.84 

29.88 

29.93 

29.98 

30.02 

30.07 

30.12 

30.16 

9.7 

30.21 

30.26 

30.30 

30.35 

30.40 

30.44 

30.49 

30.54 

30.58 

30.63 

9.8 

30.68 

30.73 

30.77 

30.82 

30.87 

30.91 

30.96 

31.01 

31.06 

31.10 

9.9 

31.15 

31.20 

31.24 

31.29 

31.34 

31.38 

31.43 

31.48 

31.53 

31.58 

10.0 

31.62 

31.67 

31.72 

31.77 

31.81 

31.86 

31.91 

31.96 

32.00 

32.05 

MISCELLANEOUS  TABLES  AND  DATA 


291 


TABLE  64 

CONVENTIONAL  SIGNS  FOR  IRRIGATION  STRUCTURES 
Adopted  by  U.  S.  Reclamation  Service 


Dam 

Diversion  dam  or  weir 

Headworks. .  1s 

* 

Tunnel 

II 

•,       * 
Bridge ^= 

Spillway ^Jlj 

Drainage  culvert  under  canal — Mf^ 

IP 

Box  or  pipe  culvert  under  road ^ 

Flume 

Check  or  drop A 

Siphon  or  covered  conduit 

/Jv 

Sluiceway - "C|- 

Turnout =^-(1) 

Telephones |    |     i 

Telephone  line _4 

Transmission  line  . 


292 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  65 

SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS,  AND  AREA 
AND  CIRCUMFERENCE  OF  CIRCLES  OF  RADIUS  N 


N 

AT' 

N* 

N* 

yi 

1 

N 

7T.ZV2 

2  *N 

1 

1 

1 

1.0000 

1.0000 

1.000000 

3.142 

6.283 

2 

4 

8 

1.4142 

1.2599 

.500000 

12.566 

12.566 

3 

9 

27 

1.7321 

1.4422 

.333333 

28.274 

18.850 

4 

16 

64 

2.0000 

1.5874 

.250000 

50.265 

25.133 

5 

25 

125 

2.2361 

1.7100 

.200000 

78.540 

31.416 

6 

36 

216 

2.4495 

1.8171 

.166667 

113.097 

37.699 

7 

49 

343 

2.6458 

1.9129 

.142857 

153.938 

43.982 

8 

64 

512 

2.8284 

2.0000 

.125000 

201.062 

50.265 

9 

81 

729 

3.0000 

2.0801 

.111111 

254.469 

56.549 

10 

100 

1,000 

3.1623 

2.1544 

.100000 

314.159 

62.832 

11 

121 

1,331 

3.3166 

2.2240 

.090909 

380.133 

69.115 

12 

144 

1,728 

3.4641 

2.2894 

.083333 

452.389 

75.398 

13 

169 

2,197 

3.6056 

2.3513 

.076923 

530.929 

81.681 

14 

196 

2,744 

3.7417 

2.4101 

.071429 

615.752 

87.965 

15 

225 

3,375 

3.8730 

2.4662 

.066667 

706.858 

94.248 

16 

256 

4,096 

4.0000 

2.5198 

.062500 

804.248 

100.531 

17 

289 

4,913 

4.1231 

2.5713 

.058824 

907.920 

106.814 

18 

324 

5,832 

4.2426 

2.6207 

.055556 

1,017.876 

113.097 

19 

361 

6,859 

4.3589 

2.6684 

.052632 

1,134.115 

119.381 

20 

400 

8,000 

4.4721 

2.7144 

.050000 

1,256.637 

125.664 

21 

441 

9,261 

4.5826 

2.7589 

.047619 

1,385.442 

131.947 

22 

484 

10,648 

4.6904 

2.8020 

.045455 

1,520.531 

138.230 

23 

529 

12,167 

4.7958 

2.8439 

.043478 

1,661.903 

144.513 

24 

576 

13,824 

4.8990 

2.8845 

.041667 

1,809.557 

150.796 

25 

625 

15,625 

5.0000 

2.9240 

.040000 

1,963.495 

157.080 

26 

676 

17,576 

5.0990 

2.9625 

.038462 

2,123.717 

163.363 

27 

729 

19,683 

5.1962 

3.0000 

.037037 

2,290.221 

169.646 

28 

784 

21,952 

5.2915 

3.0366 

.035714 

2,463.009 

175.929 

29 

841 

24,389 

5.3852 

3.0723 

.034483 

2,642.079 

182.212 

30 

900 

27,000 

5.4772 

3.1072 

.033333 

2,827.433 

188.496 

31 

961 

29,791 

5.5678 

3.1414 

.032258 

3,019.071 

194.779 

32 

1,024 

32,768 

5.6569 

3.1748 

.031250 

3,216.991 

201.062 

33 

1,089 

35,937 

5.7446 

3.2075 

.030303 

3,421.194 

207.345 

34 

1,156 

39,304 

5.8310 

3.2396 

.029412 

3,631.681 

213  .,628 

35 

1,225 

42,875 

5.9161 

3.2711 

.028571 

3,848.451 

219.911 

36 

1,296 

46,656 

6.0000 

3.3019 

.027778 

4,071.504 

226.195 

37 

1,369 

50,653 

6.0828 

3.3322 

.027027 

4,300.840 

232.478 

38 

1,444 

54,872 

6.1644 

3.3620 

.026316 

4,536.460 

238.761 

39 

1,521 

59,319 

6.2450 

3.3912 

.025641 

4,778.362 

245.044 

40 

1,600 

64,000 

6.3246 

3.4200 

.025000 

5,026.548 

251.327 

41 

1,681 

68,921 

6.4031 

3.4482 

.024390 

5,281.017 

257.611 

42 

1,764 

74,088 

6.4807 

3.4760 

.023810 

5,541.770 

263.894 

43 

1,849 

79,507 

6.5574 

3.5034 

.023256 

5,808.805 

270.177 

44 

1,936 

85,184 

6.6332 

3.5303 

.022727 

6,082.123 

276.460 

45 

2,025 

91,125 

6.7082 

3.5569 

.022222 

6,361.725 

282.743 

46 

2,116 

97,336 

6.7823 

3.5830 

.021739 

6,647.610 

289.027 

47 

2,209 

103,823 

6.8557 

3.6088 

.021277 

6,939.778 

295.310 

48 

2,304 

110,592 

6.9282 

3.6342 

.020833 

7,238.230 

301.593 

49 

2,401 

117,649 

7.0000 

3.6593 

.020408 

7,542.964 

307.876 

50 

2,500 

125,000 

7.0711 

3.6840 

.020000 

7,853.982 

314.159 

MISCELLANEOUS   TABLES   AND   DATA 


293 


TABLE   65  (Continued) 

SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS,  AND  AREA 
AND  CIRCUMFERENCE  OF  CIRCLES  OF  RADIUS  N 


N 

N2 

N3 

B* 

N* 

i 

N 

7J-2V2 

2  nN 

51 

2,601 

132,651 

7.1414 

3.7084 

.019607 

8,171.283 

320.442 

52 

2,704 

140,608 

7.2111 

3.7325 

.019231 

8,494.867 

326.726 

53 

2,809 

148,877 

7.2801 

3.7563 

.018868 

8,824.734 

333.009 

54 

2,916 

157,464 

7.3485 

3.7798 

.018519 

9,160.884 

339.292 

55 

3,025 

166,375 

7.4162 

3.8030 

.018182 

9,503.318 

345.575 

56 

3,136 

175,616 

7.4833 

3.8259 

.017857 

9,852.035 

351.858 

57 

3,249 

185,193 

7.5498 

3.8485 

.017544 

10,207.035 

358.142 

58 

3,364 

195,112 

7.6158 

3.8709 

.017241 

10,568.318 

364.425 

59 

3,481 

205,379 

7.6811 

3.8930 

.016949 

10,935.884 

370.708 

60 

3,600 

216,000 

7.7460 

3.9149 

.016667 

11,309.734 

376.991 

61 

3,721 

226,981 

7.8102 

3.9365 

.016393 

11,689.866 

383.274 

62 

3,844 

238,328 

7.8740 

3.9579 

.016129 

12,076.282 

389.557 

63 

3,969 

250,047 

7.9373 

3.9791 

.015873 

12,468.981 

395.841 

64 

4,096 

262,144 

8.0000 

4.0000 

.015625 

12,867.964 

402.124 

65 

4,225 

274,625 

8.0623 

4.0207 

.015385 

13,273.229 

408.407 

66 

4,356 

287,496 

8.1240 

4.0412 

.015156 

13,684.778 

414.690 

67 

4,489 

300,763 

8.1854 

4.0615 

.014925 

14,102.610 

420.973 

68 

4,624 

314,432 

8,2462 

4.0817 

.014706 

14,526.725 

427.257 

69 

4,761 

328,509 

8.3066 

4.1016 

.014493 

14,957.123 

433.540 

70 

4,900 

343,000 

8.3666 

4.1213 

.014286 

15,393.804 

439.823 

71 

5,041 

357,911 

8.4261 

4.1408 

.014085 

15,836.769 

446.106 

72 

5,184 

373,248 

8.4853 

4.1602 

.013889 

16,286.017 

452.389 

73 

5,329 

389,017 

8.5440 

4.1793 

.013699 

16,741.547 

458.673 

74 

5,476 

405,224 

8.6023 

4.1983 

.013514 

17,203.362 

464.956 

75 

5,625 

421,875 

8.6603 

4.2172 

.013333 

17,671.459 

471.239 

76 

5,776 

438,976 

8.7178 

4.2358 

.013158 

18,145.839 

477.522 

77 

5,929 

456,533 

8.7750 

4.2543 

.012987 

18,626.503 

483.805 

78 

6,084 

474,552 

8.8318 

4.2727 

.012821 

19,113.450 

490.088 

79 

6,241 

493,039 

8.8882 

4.2908 

.012658 

19,606.680 

486.372 

80 

6,400 

512,000 

8.9443 

4.3089 

.012500 

20,106.193 

502.655 

81 

6,561 

531,441 

9.0000 

4.3267 

.012346 

20,611.990 

508.938 

82 

6,724 

551,368 

9.0554 

4.3445 

.012195 

21,124.069 

515.221 

83 

6,889 

571,787 

9.1104 

4.3621 

.012048 

21,642.432 

521.504 

84 

7,056 

592,704 

9.1652 

4.3795 

.011905 

22,167.078 

527.788 

85 

7,225 

614,125 

9.2195 

4.3968 

.011765 

22,698.007 

534.071 

86 

7,396 

636,056 

9.2736 

4.4140 

.011628 

23,235.220 

540.354 

87 

7,569 

658,503 

9.3274 

4.4310 

.011494 

23,778.715 

546.637 

88 

7,744 

681,472 

9.3808 

4.4480 

.011364 

24,328.494 

552.920 

89 

7,921 

704,969 

9.4340 

4.4647 

.011236 

24,884.556 

559.205 

90 

8,100 

.729,000 

9.4868 

4.4814 

.011111 

25,446.901 

565.487 

91 

8,281 

753,571 

9.5394 

4.4979 

.010989 

26,015.529 

571.770 

92 

8,464 

778,688 

9.5917 

4.5144 

.010870 

26,590.441 

578.053 

93 

8,649 

804,357 

9.6437 

4.5307 

.010753 

27,171.635 

584.336 

94 

8,836 

830,584 

9.6954 

4.5468 

.010638 

27,759.113 

590.619 

95 

9,025 

857,375 

9.7468 

4.5629 

.010526 

28,352.874 

596.903 

96 

9,216 

884,736 

9.7980 

4.5789 

.010417 

28,952.918 

603.186 

97 

9,409 

912,673 

9.8489 

4.5947 

.010309 

29,559.246 

609.469 

98 

9,604 

941,192 

9.8995 

4.6104 

.010204 

30,171.856 

615.752 

99 

9,801 

970,299 

9.9499 

4.6261 

.010101 

30,790.750 

622.035 

100 

10,000 

1,000,000 

10.0000 

4.6416 

.010000 

31,415.927 

628.319 

294 


WORKING    DATA    FOR    IRRIGATION    ENGINEERS 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

N* 

W 

N* 

N* 

l 

N 

101 

10,201 

1,030,301 

10.0498756 

4.6570095 

.009900990 

102 

10,404 

1,061,208 

10.0995049 

4.6723287 

.009803922 

103 

10,609 

1,092,727 

10.1488916 

4.6875482 

.009708738 

104 

10,816 

1,124,864 

10.1980390 

4.7026694 

.009615385 

105 

11,025 

1,157,625 

10.2469508 

4.7176940 

.009523810 

106 

11,236 

1,191,016 

10.2956301 

4.7326235 

.009433962 

107 

11,449 

1,225,043 

10.3440804 

4.7474594 

.009345794 

108 

11,664 

1,259,712 

10.3923048 

4.7622032 

.009259259 

109 

11,881 

1,295,029 

10.4403065 

4.7768562 

.009174312 

110 

12,100 

1,331,000 

10.4880885 

4.7914199 

.009090909 

111 

12,321 

1,367,631 

10.5356538 

4.8058955 

.009009009 

112 

12,544 

1,404,928 

10.5830052 

4.8202845 

.008928571 

113 

12,769 

1,442,897 

10.6301458 

4.8345881 

.008849558 

114 

12,996 

1,481,544 

10.6770783 

4.8488076 

.008771930 

115 

13,225 

1,520,875 

10.7238053 

4.8629442 

.008695652 

116 

13,456 

1,560,896 

10.7703296 

4.8769990 

.008620690 

117 

13,689 

1,601,613 

10.8166538 

4.8909732 

.008547009 

118 

13,924 

1,643,032 

10.8627805 

4.9048681 

.008474576 

119 

14,161 

1,685,159 

10.9087121 

4.9186847 

.008403361 

120 

14,400 

1,728,000 

10.9544512 

4.9324242 

.008333333 

121 

14,641 

1,771,561 

11.0000000 

4.9460874 

.008264463 

122 

14,884 

1,815,848 

11.0453610 

4.9596757 

.008196721 

123 

15,129 

1,860,867 

11.0905365 

4.9731898 

.008130081 

124 

15,376 

1,906,624 

11.1355287 

4.9866310 

.008064516 

125 

15,625 

1,953,125 

11.1803399 

5.0000000 

.008000000 

126 

15,876 

2,000,376 

11.2249722 

5.0132979 

.007936508 

127 

16,129 

2,048,383 

11.2694277 

5.0265257 

.007874016 

128 

16,384 

2,097,152 

11.3137085 

5.0396842 

.007812500 

129 

16,641 

2,146,689 

11.3578167 

5.0527743 

.007751938 

130 

16,900 

2,197,000 

11.4017543 

5.0657970 

.007692308 

131 

17,161 

2,248,091 

11.4455231 

5.0787531 

.007633588 

132 

17,424 

2,299,968 

11.4891253 

5.0916434 

.007575758 

133 

17,689 

2,352,637 

11.5325626 

5.1044687 

.007518797 

134 

17,956 

2,406,104 

11.5758369 

5.1172299 

.007462687 

135 

18,225 

2,460,375 

11.6189500 

5.1299278 

.007407407 

136 

18,496 

2,515,456 

11.6619038 

5.1425632 

.007352941 

137 

18,769 

2,571,353 

11.7046999 

5.1551367 

.007299270 

138 

19,044 

2,628,072 

11.7473401 

5.1676493 

.007246377 

139 

19,321 

2,685,619 

11.7898261 

5.1801015 

.007194245 

140 

19,600 

2,744,000 

11.8321596 

5.1924941 

.007142857 

141 

19,881 

2,803,221 

11.8743421 

5.2048279 

.007092199 

142 

20,164 

2,863,288 

11.9163753 

5.2171034 

.007042254 

143 

20,449 

2,924,207 

11.9582607 

5.2293215 

.006993007 

144 

20,736 

2,985,984 

12.0000000 

5.2414828 

.006944444 

145 

21,025 

3,048,625 

12.0415946 

5.2535879 

.006896552 

146 

21,316 

3,112,136 

12.0830460 

5.2656374 

.006849315 

147 

21,609 

3,176,523 

12.1243557 

5.2776321 

.006802721 

148 

21,904 

3,241,792 

12.1655251 

5.2895725 

.006756757 

149 

22,201 

3,307,949 

12.2065556 

5.3014592 

.006711409 

150 

22,500 

3,375,000 

12.2474487 

5.3132928 

.006666667 

MISCELLANEOUS   TABLES   AND   DATA 


295 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


2V 

N2 

AT3 

•** 

N* 

1 

N 

151 

22,801 

3,442,951 

12.2882057 

5.3250740 

.006622517 

152 

23,104 

3,511,808 

12.3288280 

5.3368033 

.006578947 

153 

23,409 

3,581,577 

12.3693769 

5.3484812 

.006535948 

154 

23,716 

3,652,264 

12.4096736 

5.3601084 

.006493506 

155 

24,025 

3,723,875 

12.4498996 

5.3716854 

.006451613 

156 

24,336 

3,796,416 

12.4899960 

5.3832126 

.006410256 

157 

24,649 

3,869,893 

12.5299641 

5.3946907 

.006369427 

158 

24,964 

3,944,312 

12.5698051 

5.4061202 

.006329114 

159 

25,281 

4,019,679 

12.6095202 

5.4175015 

.006289308 

160 

25,600 

4,096,000 

12.6491106 

5.4288352 

.006250000 

161 

25,921 

4,173,281 

12.6885775 

5.4401218 

.006211180 

162 

26,244 

4,251,528 

12.7279221 

5.4513618 

.006172840 

163 

26,569 

4,330,747 

12.7671453 

5.4625556 

.006134969 

164 

26,896 

4,410,944 

12.8062485 

5.4737037 

.006097561 

165 

27,225 

4,492,125 

12.8452326 

5.4848066 

.006060606 

166 

27,556 

4,574,296 

12.8840987 

5.4958647 

.006024096 

167 

27,889 

4,657,463 

12.9228480 

5.5068784 

.005988024 

168 

28,224 

4,741,632 

12.9614814 

5.5178484 

.005952381 

169 

28,561 

4,826,809 

13.0000000 

5.5287748 

.005917160 

170 

28,900 

4,913,000 

13.0384048 

5.5396583 

.005882353 

171 

29,241 

5,000,211 

13.0766968 

5.5504991 

.005847953 

172 

29,584 

5,088,448 

13.1148770 

5.5612978 

.005813953 

173 

29,929 

5,177,717 

13.1529464 

5.5720546 

.005780347 

174 

30,276 

5,268,024 

13.1909060 

5.5827702 

.005747126 

175 

30,625 

5,359,375 

13.2287566 

5.5934447 

.005714286 

176 

30,976 

5,451,776 

13.2664992 

5.6040787 

.005681818 

177 

31,329 

5,545,233 

13.3041347 

5.6146724 

.005649718 

178 

31,684 

5,639,752 

13.3416641 

5.6252263 

.005617978 

179 

32,041 

5,735,339 

13.3790882 

5.6357408 

.005586592 

180 

32,400 

5,832,000 

13.4164079 

5.6462162 

.005555556 

181 

32,761 

5,929,741 

13.4536240 

5.6566528 

.005524862 

182 

33,124 

6,028,568 

13.4907376 

5.6670511 

.005494505 

183 

33,489 

6,128,487 

13.5277493 

5.6774114 

.005464481 

184 

33,856 

6,229,504 

13.5646600 

5.6877340 

.005434783 

185 

34,225 

6,331,625 

13.6014705 

5.6980192 

.005405405 

186 

34,596 

6,434,856 

13.6381817 

5.7082675 

.005376344 

187 

34,969 

6,539,203 

13.6747943 

5.7184791 

.005347594 

188 

35,344 

6,644,672 

13.7113092 

5.7286543 

.005319149 

189 

35,721 

6,751,269 

13.7477271 

5.7387936 

.005291005 

190 

36,100 

6,859,000 

13.7840488 

5.7488971 

.005263158 

191 

36,481 

6,967,871 

13.8202750 

5.7589652 

.005235602 

192 

36,864 

7,077,888 

13.8564065 

5.7689982 

.005208333 

193 

37,249 

7,189,057 

13.8924440 

5.7789966 

.005181347 

194 

37,636 

7,301,384 

13.9283883 

5.7889604 

.005154639 

195 

38,025 

7,414,875 

13.9642400 

5.7988900 

.005128205 

196 

38,416 

7,529,536 

14.0000000 

5.8087857 

.005102041 

197 

38,809 

7,645,373 

14.0356688 

5.8186479 

.005076142 

198 

39,204 

7,762,392 

14.0712473 

5.8284767 

.005050505 

199 

39,610 

7,880,599 

14.1067360 

5.8382725 

.005025126 

200 

40,000 

8,000,000 

14.1421356 

5.8480355 

.005000000 

296 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

N* 

NI 

N* 

** 

l 
N 

201 

40,401 

8,120,601 

14.1774469 

5.8577660 

.004975124 

202 

40,804 

8,242,408 

14.2126704 

5.8674643 

.004950495 

203 

41,209 

8,365,427 

14.2478068 

5.8771307 

.004926108 

204 

41,616 

8,489,664 

14.2828569 

5.8867653 

.004901961 

205 

42,025 

8,615,125 

14.3178211 

5.8963685 

.004878049 

206 

42,436 

8,741,816 

14.3527001 

5.9059406 

.004854369 

207 

42,849 

8,869,743 

14.3874946 

5.9154817 

.004830918 

208 

43,264 

8,998,912 

14.4222051 

5.9249921 

.004807692 

209 

43,681 

9,129,329 

14.4568323 

5.9344721 

.004784689 

210 

44,100 

9,261,000 

14.4913767 

5.9439220 

.004761905 

211 

44,521 

9,393,931 

14.5258390 

5.9533418 

.004739336 

212 

44,944 

9,528,128 

14.5602198 

5.9627320 

.004716981 

213 

45,369 

9,663,597 

14.5945195 

5.9720926 

.004694836 

214 

45,796 

9,800,344 

14.6287388 

5.9814240 

.004672897 

215 

46,225 

9,938,375 

14.6628783 

5.9907264 

.004651163 

216 

46,656 

10,077,696 

14.6969385 

6.0000000 

.004629630 

217 

47,089 

10,218,313 

14.7309199 

6.0092450 

.004608295 

218 

47,524 

10,360,232 

14.7648231 

6.0184617 

.004587156 

219 

47,961 

10,503,459 

14.7986486 

6.0276502 

.004566210 

220 

48,400 

10,648,000 

14.8323970 

6.0368107 

.004545455 

221 

48,841 

10,793,861 

14.8660687 

6.0459435 

.004524887 

222 

49,284 

10,941,048 

14.8996644 

6.0550489 

.004504505 

223 

49,729 

11,089,567 

14.9331845 

6.0641270 

.004484305 

224 

50,176 

11,239,424 

14.9666295 

6.0731779 

.004464286 

225 

50,625 

11,390,625 

15.0000000 

6.0822020 

.004444444 

226 

51,076 

11,543,176 

15.0332964 

6.0911994 

.004434779 

227 

51,529 

11,697,083 

15.0665192 

6.1001702 

.004405286 

228 

51,984 

11,852,352 

15.0996689 

6.1091147 

.004385965 

229 

52,441 

12,008,989 

15.1327460 

6.1180332 

.004366812 

230 

52,900 

12,167,000 

15.1657509 

6.1269257 

.004347826 

231 

53,361 

12,326,391 

15.1986842 

6.1357924 

.004329004 

232 

53,824 

12,487,168 

15.2315462 

6.1446337 

.004310345 

233 

54,289 

12,649,337 

15.2643375 

6.1534495 

.004291845 

234 

54,756 

12,812,904 

15.2970585 

6.1622401 

.004273504 

235 

55,225 

12,977,875 

15.3297097 

6.1710058 

.004255319 

236 

55,696 

13,144,256 

15.3622915 

6.1797466 

.004237288 

237 

56,169 

13,312,053 

15.3948043 

6.1884628 

.004219409 

238 

56,644 

13,481,272 

15.4272486 

6.1971544 

.004201681 

239 

57,121 

13,651,919 

15.4596248 

6.2058218 

.004184100 

240 

57,600 

13,824,000 

15.4919334 

6.2144650 

.004166667 

241 

58,081 

13,997,521 

15.5241747 

6.2230843 

.004149378 

242 

58,564 

14,172,488 

15.5563492 

6.2316797 

.004132231 

243 

59,049 

14,348,907 

15.5884573 

6.2402515 

.004115226 

244 

59,536 

14,526,784 

15.6204994 

6.2487998 

.004098361 

245 

60,025 

14,706,125 

15.6524758 

6.2573248 

.004081633 

246 

60,516 

14,886,936 

15.6843871 

6.2658266 

.004065041 

247 

61,009 

15,069,223 

15.7162336 

6.2743054 

.004048583 

248 

61,504 

15,252,992 

15.7480157 

6.2827613 

.004032258 

249 

62,001 

15,438,249 

15.7797338 

6.2911946 

.004016064 

250 

62,500 

15,625,000 

15.8113883 

6.2996053 

.004000000 

MISCELLANEOUS   TABLES   AND   DATA 


297 


TABLE  65  (Continued} 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

AT2 

N^ 

N* 

fri 

l 

N 

251 

63,001 

15,813,251 

15.8429795 

6.3079935 

.003984064 

252 

63,504 

16,003,008 

15.8745079 

6.3163596 

.003968254 

253 

64,009 

16,194,277 

15.9059737 

6.3247035 

.003952569 

254 

64,516 

16,387,064 

15.9373775 

6.3330256 

.003937008 

255 

65,025 

16,581,375 

15.9687194 

6.3413257 

.003921569 

256 

65,536 

16,777,216 

16.0000000 

6.3496042 

.003906250 

257 

66,049 

16,974,593 

16.0312195 

6.3578611 

.003891051 

258 

66,564 

17,173,512 

16.0623784 

6.3660968 

.003875969 

259 

67,081 

17,373,979 

16.0934769 

6.3743111 

.003861004 

260 

67,600 

17,576,000 

16.1245155 

6.3825043 

.003846154 

261 

68,121 

17,779,581 

16.1554944 

6.3906765 

.003831418 

262 

68,644 

17,984,728 

16.1864141 

6.3988279 

.003816794 

263 

69,169 

18,191,447 

16.2172747 

6.4069585 

.003802281 

264 

69,696 

18,399,744 

16.2480768 

6.4150687 

.003787879 

265 

70,225 

18,609,625 

16.2788206 

6.4231583 

.003773585 

266 

70,756 

18,821,096 

16.3095064 

6.4312276 

.003759398 

267 

71,289 

19,034,163 

16.3401346 

6.4392767 

.003745318 

268 

71,824 

19,248,832 

16.3707055 

6.4473057 

.003731343 

269 

72,361 

19,465,109 

16.4012195 

6.4553148 

.003717472 

270 

72,900 

19,683,000 

16.4316767 

6.4633041 

.003703704 

271 

73,441 

19,902,511 

16.4620776 

6.4712736 

.003690037 

272 

73,984 

20,123,648 

16.4924225 

6.4792236 

.003676471 

273 

74,529 

20,346,417 

16.5227116 

6.4871541 

.003663004 

274 

75,076 

20,570,824 

16.5529454 

6.4950653 

.003649635 

275 

75,625 

20,796,875 

16.5831240 

6.5029572 

.003636364 

276 

76,176 

21,024,576 

16.6132477 

6.5108300 

.003623188 

277 

76,729 

21,253,933 

16.6433170 

6.5186839 

.003610108 

278 

77,284 

21,484,952 

16.6733320 

6.5265189 

.003597122 

279 

77,841 

21,717,639 

16.7032931 

6.5343351 

.003584229 

280 

78,400 

21,952,000 

16.7332005 

6.5421326 

.003571429 

281 

78,961 

22,188,041 

16.7630546 

6.5499116 

.003558719 

282 

79,524 

22,425,768 

16.7928556 

6.5576722 

.003546099 

283 

80,089 

22,665,187 

16.8226038 

6.5654144 

.003533569 

284 

80,656 

22,906,304 

16.8522995 

6.5731385 

.003521127 

285 

81,225 

23,149,125 

16.8819430 

6.5808443 

.003508772 

286 

81,796 

23,393,656 

16.9115345 

6.5885323 

.003496503 

287 

82,369 

23,639,903 

16.9410743 

6.5962023 

.003484321 

288 

82,944 

23,887,872 

16.9705627 

6.6038545 

.003472222 

289 

83,521 

24,137,569 

17.0000000 

6.6114890 

.003460208 

290 

84,100 

24,389,000 

17.0293864 

6.6191060 

.003448276 

291 

84,681 

24,642,171 

17.0587221 

6.6267054 

.003436426 

292 

85,264 

24,897,088 

17.0880075 

6.6342874 

.003424658 

293 

85,849 

25,153,757 

17.1172428 

6.6418522 

.003412969 

294 

86,436 

25,412,184 

17.1464282 

6.6493998 

.003401361 

295 

87,025 

25,672,375 

17.1755640 

6.6569302 

.003389831 

296 

87,616 

25,934,336 

17.2046505 

6.6644437 

.003378378 

297 

88,209 

26,198,073 

17.2336879 

6.6719403 

.003367003 

298 

88,804 

26,463,592 

17.2626765 

6.6794200 

.003355705 

299 

89,401 

26,730,899 

17.2916165 

6.6868831 

.003344482 

300 

90,000 

27,000,000 

17.3205081 

6.6943295 

.003333333 

298 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

AT* 

N3 

N* 

N* 

l 
N 

301 

90,601 

27,270,901 

17.3493516 

6.7017593 

.003322259 

302 

91,204 

27,543,608 

17.3781472 

6.7091729 

.003311258 

303 

91,809 

27,818,127 

17.4068952 

6.7165700 

.003300330 

304 

92,416 

28,094,464 

17.4355958 

6.7239508 

.003289474 

305 

93,025 

28,372,625 

17.4642492 

6.7313155 

.003278689 

306 

93,636 

28,652,616 

17.4928557 

6.7386641 

.003267974 

307 

94,249 

28,934,443 

17.5214155 

6.7459967 

.003257329 

308 

94,864 

29,218,112 

17.5499288 

6.7533134 

.003246753 

309 

95,481 

29,503,629 

17.5783958 

6.7606143 

.003236246 

310 

96,100 

29,791,000 

17.6068169 

6.7678995 

.003225806 

311 

96,721 

30,080,231 

17.6351921 

6.7751690 

.003215434 

312 

97,344 

30,371,328 

17.6635217 

6.7824229 

.003205128 

313 

97,969 

30,664,297 

17.6918060 

6.7896613 

.003194888 

314 

98,596 

30,959,144 

17.7200451 

6.7968844 

.003184713 

315 

99,225 

31,255,875 

17.7482393 

6.8040921 

.003174603 

316 

99,856 

31,554,496 

17.7763888 

6.8112847 

.003164557 

317 

100,489 

31,855,013 

17.8044938 

6.8184620 

.003154574 

318 

101,124 

32,157,432 

17.8325545 

6.8256242 

.003144654 

319 

101,761 

32,461,759 

17.8605711 

6.8327714 

.003134796 

320 

102,400 

32,768,000 

17.8885438 

6.8399037 

.003125000 

321 

103,041 

33,076,161 

17.9164729 

6.8470213 

.003115265 

322 

103,684 

33,386,248 

17.9443584 

6.8541240 

.003105590 

323 

104,329 

33,698,267 

17.9722008 

6.8612120 

.003095975 

324 

104,976 

34,012,224 

18.0000000 

6.8682855 

.003086420 

325 

105,625 

34,328,125 

18.0277564 

6.8753443 

.003076923 

326 

106,276 

34,645,976 

18.0554701 

6.8823888 

.003067485 

327 

106,929 

34,965,783 

18.0831413 

6.8894188 

.003058104 

328 

107,584 

35,287,552 

18.1107703 

6.8964345 

.003048780 

329 

108,241 

35,611,289 

18.1383571 

6.9034359 

.003039514 

330 

108,900 

35,937,000 

18.1659021 

6.9104232 

.003030303 

331 

109,561 

36,264,691 

18.1934054 

6.9173964 

.003021148 

332 

110,224 

36,594,368 

18.2208672 

6.9243556 

.003012048 

333 

110,889 

36,926,037 

18.2482876 

6.9313008 

.003003003 

334 

111,556 

37,259,704 

18.2756669 

6.9382321 

.002994012 

335 

112,225 

37,595,375 

18.3030052 

6.9451496 

.002985075 

336 

112,896 

37,933,056 

18.3303028 

6.9520533 

.002976190 

337 

113,569 

38,272,753 

18.3575598 

6.9589434 

.002967359 

338 

114,244 

38,614,472 

18.3847763 

6.9658198 

.002958580 

339 

114,921 

38,958,219 

18.4119526 

6.9726826 

.002949853 

340 

115,600 

39,304,000 

18.4390889 

6.9795321 

.002941176 

341 

116,281 

39,651,821 

18.4661853 

6.9863681 

.002932551 

342 

116,964 

40,001,688 

18.4932420 

6.9931906 

.002923977 

343 

117,649 

40,353,607 

18.  5202532 

7.0000000 

.002915452 

344 

118,336 

40,707,584 

18.5472370 

7.0067962 

.002906977 

345 

119,025 

41,063,625 

18.5741756 

7.0135791 

.002898551 

346 

119,716 

41,421,736 

18.6010752 

7.0203490 

.002890173 

347 

120,409 

41,781,923 

18.6279360 

7.0271058 

.002881844 

348 

121,104 

42,144,192 

18.6547581 

7.0338497 

.002873563 

349 

121,801 

42,508,549 

18.6815417 

7.0405806 

.002865330 

350 

122,500 

42,875,000 

18.7082869 

7.0472987 

.002857143 

MISCELLANEOUS   TABLES   AND  DATA 


299 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


§ 

1 

1 

N 

N2 

N3 

N* 

N 

351 

123,201 

43,243,551 

18.7349940 

7.0540041 

.002849003 

352 

123,904 

43,614,208 

18.7616630 

7.0606967 

.002840909 

353 

124,609 

43,986,977 

18.7882942 

7.0673767 

.002832861 

354 

125,316 

44,361,864 

18.8148877 

7.0740440 

.002824859 

355 

126,025 

44,738,875 

18.8414437 

7.0806988 

.002816901 

356 

126,736 

45,118,016 

18.8679623 

7.0873411 

.002808989 

357 

127,449 

45,499,293 

18.8944436 

7.0939709 

.002801120 

358 

128,164 

45,882,712 

18.9208879 

7.1005885 

.002793296 

359 

128,881 

46,268,279 

18.9472953 

7.1071937 

.002785515 

360 

129,600 

46,656,000 

18.9736660 

7.1137866 

.002777778 

361 

130,321 

47,045,881 

19.0000000 

7.1203674 

.002770083 

362 

131,044 

47,437,928 

19.0262976 

7.1269360 

.002762431 

363 

131,769 

47,832,147 

19.0525589 

7.1334925 

.002754821 

364 

132,496 

48,228,544 

19.0787840 

7.1400370 

.002747253 

365 

133,225 

48,627,125 

19.1049732 

7.1465695 

.002739726 

366 

133,956 

49,027,896 

19.1311265 

7.1530901 

.002732240 

367 

134,689 

49,430,863 

19.1572441 

7.1595988 

.002724796 

368 

135,424 

49,836,032 

19.1833261 

7.1660957 

.002717391 

369 

136,161 

50,243,409 

19.2093727 

7.1725809 

.002710027 

370 

136,900 

50,653,000 

19.2353841 

7.1790544 

.002702703 

371 

137,641 

51,064,811 

19.2613603 

7.1855162 

.002695418 

372 

138,384 

51,478,848 

19.2873015 

7:1919663 

.002688172 

373 

139,129 

51,895,117 

19.3132079 

7.1984050 

.002680965 

374 

139,876 

52,313,624 

19.3390796 

7.2048322 

.002673797 

375 

140,625 

52,734,375 

19.3649167 

7.2112479 

.002666667 

376 

141,376 

53,157,376 

19.3907194 

7.2176522 

.002659574 

377 

142,129 

53,582,633 

19.4164878 

7.2240450 

.002652520 

378 

142,884 

54,010,152 

19.4422221 

7.2304268 

.002645503 

379 

143,641 

54,439,939 

19.4679223 

7.2367972 

.002638522 

380 

144,400 

54,872,000 

19.4935887 

7.2431565 

.002631579 

381 

145,161 

55,306,341 

19.5192213 

7.2495045 

.002624672 

382 

145,924 

55,742,968 

19.5448203 

7.2558415 

.002617801 

383 

146,689 

56,181,887 

19.5703858 

7.2621675 

.002610966 

384 

147,456 

56,623,104 

19.5959179 

7.2684824 

.002604167 

385 

148,225 

57,066,625 

19.6214169 

7.2747864 

.002597403 

386 

148,996 

57,512,456 

19.6468827 

7.2810794 

.002590674 

387 

149,769 

57,960,603 

19.6723156 

7.2873617 

.002583979 

388 

150,544 

58,411,072 

19.6977156 

7.2936330 

.002577320 

389 

151,321 

58,863,869 

19.7230829 

7.2998936 

.002570694 

390 

152,100 

59,319,000 

19.7484177 

7.3061436 

.002564103 

391 

152,881 

59,776,471 

19.7737199 

7.3123828 

.002557545 

392 

153,664 

60,236,288 

19.7989899 

7.3186114 

.002551020 

393 

154,449 

60,698,457 

19.8242276 

7.3248295 

.002544529 

394 

155,236 

61,162,984 

19.8494332 

7.3310369 

.002538071 

395 

156,025 

61,629,875 

19.8746069 

7.3372339 

.002531646 

396 

156,816 

62,099,136 

19.8992487 

7.3434205 

.002525253 

397 

157,609 

62,570,773 

19.9248588 

7.3495966 

.002518892 

398 

158,404 

63,044,792 

19.9499373 

7.3557624 

.002512563 

399 

159,201 

63,521,199 

19.9749844 

7.3619178 

.002506266 

400 

160,000 

64,000,000 

20.0000000 

7.3680630 

.002500000 

300 


WORKING  DATA   FOR  IRRIGATION  ENGINEERS 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

y* 

jft 

N* 

N* 

l 

N 

401 

160,801 

64,481,201 

20.0249844 

7.3741979 

.002493766 

402 

161,604 

64,964,808 

20.0499377 

7.3803227 

.002487562 

403 

162,409 

65,450,827 

20.0748599 

7.3864373 

.002481390 

404 

163,216 

65,939,264 

20.0997512 

7.3925418 

.002475248 

405 

164,025 

66,430,125 

20.1246118 

7.3986363 

.002469136 

406 

164,836 

66,923,416 

20.1494417 

7.4047206 

.002463054 

407 

165,649 

67,419,143 

20.1742410 

7.4107950 

.002457002 

408 

166,464 

67,917,312 

20.1990099 

7.4168595 

.002450980 

409 

167,281 

68,417,929 

20.2237484 

7.4229142 

.002444988 

410 

168,100 

68,921,000 

20.2484567 

7.4289589 

.002439024 

411 

168,921 

69,426,531 

20.2731349 

7.4349938 

.002433090 

412 

169,744 

69,934,528 

20.2977831 

7.4410189 

.002427184 

413 

170,569 

70,444,997 

20.3224014 

7.4470342 

.002421308 

414 

171,396 

70,957,944 

20.3469899 

7.4530399 

.002415459 

415 

172,225 

71,473,375 

20.3715488 

7.4590359 

.002409639 

416 

173,056 

71,991,296 

20.3960781 

7.4650223 

.002403846 

417 

173,889 

72,511,713 

20.4205779 

7.4709991 

.002398082 

418 

174,724 

73,034,632 

20.4450483 

7.4769664 

.002392344 

419 

175,561 

73,560,059 

20.4694895 

7.4829242 

.002386635 

420 

176,400 

74,088,000 

20.4939015 

7.4888724 

.002380952 

421 

177,241 

74,618,461 

20.5182845 

7.4948113 

.002375297 

422 

178,084 

75,151,448 

20.5426386 

7.5007406 

.002369668 

423 

178,929 

75,686.967 

20.5669638 

7.5066607 

.002364066 

424 

179,776 

76,225,024 

20.5912603 

7.5125715 

.002358491 

425 

180,625 

76,765,625 

20.6155281 

7.5184730 

.002352941 

426 

181,476 

77,308,776 

20.6397674 

7.5243652 

.002347418 

427 

182,329 

77,854,483 

20.6639783 

7.5302482 

.002341920 

428 

183,184 

78,402,752 

20.6881609 

7.5361221 

.002336449 

429 

184,041 

78,953,589 

20.7123152 

7.5419867 

.002331002 

430 

184,900 

79,507,000 

20.7364414 

7.5478423 

.002325581 

431 

185,761 

80,062,991 

20.7605395 

7.5536888 

.002320186 

432 

186,624 

80,621,568 

20.7846097 

7.5595263 

.002314815 

433 

187,489 

81,182,737 

20.8086520 

7.5653548 

.002309469 

434 

188,356 

81,746,504 

20.8326667 

7.5711743 

.002304147 

435 

189,225 

82,312,875 

20.8566536 

7.5769849 

.002298851 

436 

190,096 

82,881,856 

20.8806130 

7.5827865 

.002293578 

437 

190,969 

83,453,453 

20.9045450 

7.5885793 

.002288330 

438 

191,844 

84,027,672 

20.9284495 

7.5943633 

.002283105 

439 

192,721 

84,604,519 

20.9523268 

7.6001385 

.002277904 

440 

193,600 

85,184,000 

20.9761770 

7.6059049 

.002272727 

441 

194,481 

85,766,121 

21.0000000 

7.6116626 

.002267574 

442 

195,364 

86,350,888 

21.0237960 

7.6174116 

.002262443 

443 

196,249 

86,938,307 

21.0475652 

7.6231519 

.002257336 

444 

197,136 

87,528,384 

21.0713075 

7.6288837 

.002252252 

445 

198,025 

88,121,125 

21.0950231 

7.6346067 

.002247191 

446 

198,916 

88,716,536 

21.1187121 

7.6403213 

.002242152 

447 

199,809 

89,314,623 

21.1423745 

7.6460272 

.002237136 

448 

200,704 

89,915,392 

21.1660105 

7.6517247 

.002232143 

449 

201,601 

90,518,849 

21.1896201 

7.6574138 

.002227171 

450 

202,500 

91,125,000 

21.2132034 

7.6630943 

.002222222 

MISCELLANEOUS    TABLES   AND   DATA 


301 


TABLE   65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

jft 

2V3 

N? 

N* 

l 

N 

451 

203,401 

91,733,851 

21.2367606 

7.6687665 

.002217295 

452 

204,304 

92,345,408 

21.2602916 

7.6744303 

.002212389 

453 

205,209 

92,959,677 

21.2837967 

7.6800857  • 

.002207506 

454 

206,116 

93,576,664 

21.3072758 

7.6857328 

.002202643 

455 

207,025 

94,196,375 

21.3307290 

7.6913717 

.002197802 

456 

207,936 

94,818,816 

21.3541565 

7.6970023 

.002192982 

457 

208,849 

95,443,993 

21.3775583 

7.7026246 

.002188184 

458 

209,764 

96,071,912 

21.4009346 

7.7082388 

.002183406 

459 

210,681 

96,702,579 

21.4242853 

7.7138448 

.002178649 

460 

211,600 

97,336,000 

21.4476106 

7.7194426 

.002173913 

461 

212,521 

97,972,181 

21.4709106 

7.7250325 

.002169197 

462 

213,444 

98,611,128 

21.4941853 

7.7306141 

.002164502 

463 

214,369 

99,252,847 

21.5174348 

7.7361877 

.002159827 

464 

215,296 

99,897,344 

21.5406592 

7.7417532 

.002155172 

465 

216,225 

100,544,625 

21.5638587 

7.7473109 

.002150538 

466 

217,156 

101,194,696 

21.5870331 

7.7528606 

.002145923 

467 

218,089 

101,847,563 

21.6101828 

7.7584023 

.002141328 

468 

219,024 

102,503,232 

21.6333077 

7.7639361 

.002136752 

469 

219,961 

103,161,709 

21.6564078 

7.7694620 

.002132196 

470- 

220,900 

103,823,000 

21.6794834 

7.7749801 

.002127660 

471 

221,841 

104,487,111 

21.7025344 

7.7804904 

.002123142 

472 

222,784 

105,154,048 

21.7255610 

7.7859928 

.002118644 

473 

223,729 

105,823,817 

21.7485632 

7.7914875 

.002114165 

474 

224,676 

106,496,424 

21.7715411 

7.7969745 

.002109705 

475 

225,625 

107,171,875 

21.7944947 

7.8024538 

.002105263 

476 

226,576 

107,850,176 

21.8174242 

7.8079254 

.002100840 

477 

227,529 

108,531,333 

21.8403297 

7.8133892 

.002096436 

478 

228,484 

109,215,352 

21.8632111 

7.8188456 

.002092050 

479 

229,441 

109,902,239 

21.8860686 

7.8242942 

.002087683 

480 

230,400 

110,592,000 

21.9089023 

7.8297353 

.002083333 

481 

231,361 

111,284,641 

21.9317122 

7.8351688 

.002079002 

482 

232,324 

111,980,168 

21.9544984 

7.8405949 

.002074689 

483 

233,289 

112,678,587 

21.9772610 

7.8460134 

.002070393 

484 

234,256 

113,379,904 

22.0000000 

7.8514244 

.002066116 

485 

235,225 

114,084,125 

22.0227155 

7.8568281 

.002061856 

486 

236,196 

114,791,256 

22.0454077 

7.8622242 

.002057613 

487 

237,169 

115,501,303 

22.0680765 

7.8676130 

.002053388 

488 

238,144 

116,214,272 

22.0907220 

7.8729944 

.002049180 

489 

239,121 

116,930,169 

22.1133444 

7.8783684 

.002044990 

490 

240,100 

117,649,000 

22.1359436 

7.8837352 

.002040816 

491 

241,081 

118,370,771 

22.1585198 

7.8890946 

.002036660 

492 

242,064 

119,095,488 

22.1810730 

7.8944468 

.002032520 

493 

243,049 

119,823,157 

22.2036033 

7.8997917 

.002028398 

494 

244,036 

120,553,784 

22.2261108 

7.9051294 

.002024291 

495 

245,025 

121,287,375 

22.2485955 

7.9104599 

.002020202 

496 

246,016 

122,023,936 

22.2710575 

7.9157832 

.002016129 

497 

247,009 

122,763,473 

22.2934968 

7.9210994 

.002012072 

498 

248,004 

123,505,992 

22.3159136 

7.9264085 

.002008032 

499 

249,001 

124,251,499 

22.3383079 

7.9317104 

.002004008 

500 

250,000 

125,000,000 

22.3606798 

7.9370053 

.002000000 

302 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

#2 

N3 

N* 

N* 

l 

N 

501 

251,001 

125,751,501 

22.3830293 

7.9422931 

.001996008 

502 

252,004 

126,506,008 

22.4053565 

7.9475739 

.001992032 

503 

253,009 

127,263,527 

22.4276615 

7.9528477 

.001988072 

504 

254,016 

128,024,064 

22.4499443 

7.9581144 

.001984127 

505 

255,025 

128,787,625 

22.4722051 

7.9633743 

.001980198 

506 

256,036 

129,554,216 

22.4944438 

7.9686271 

.001976285 

507 

257,049 

130,323,843 

22.5166605 

7.9738731 

.001972387 

508 

258,064 

131,096,512 

22.5388553 

7.9791122 

.001968504 

509 

259,081 

131,872,229 

22.5610283 

7.9843444 

.001964637 

510 

260,100 

132,651,000 

22.5831796 

7.9895697 

.001960784 

511 

261,121 

133,432,831 

22.6053091 

7.9947883 

.001956947 

512 

262,144 

134,217,728 

22.6274170 

8.0000000 

.001953125 

513 

263,169 

135,005,697 

22.6495033 

8.0052049 

.001949318 

514 

264,196 

135,796,744 

22.6715681 

8.0104032 

.001945525 

515 

265,225 

136,590,875 

22.6936114 

8.0155946 

.001941748 

516 

266,256 

137,388,096 

22.7156334 

8.0207794 

.001937984 

517 

267,289 

138,188,413 

22.7376340 

8.0259574 

.001934236 

518 

268,324 

138,991,832 

22.7596134 

8.0311287 

.001930502 

519 

269,361 

139,798,359 

22.7815715 

8.0362935 

.001926782 

520 

270,400 

140,608,000 

22.8035085 

8.0414515 

.001923077 

521 

271,441 

141,420,761 

22.8254244 

8.0466030 

.001919386 

522 

272,484 

142,236,648 

22.8473193 

8.0517479 

.001915709 

523 

273,529 

143,055,667 

22.8691933 

8.0568862 

.001912046 

524 

274,576 

143,877,824 

22.8910463 

8.0620180 

.001908397 

525 

275,625 

144,703,125 

22.9128785 

8.0671432 

.001904762 

526 

276,676 

145,531,576 

22.9346899 

8.0722620 

.001901141 

527 

277,729 

146,363,183 

22.9564806 

8.0773743 

.001897533 

528 

278,784 

147,197,952 

22.9782506 

8.0824800 

.001893939 

529 

279,841 

148,035,889 

23.0000000 

8.0875794 

.001890359 

530 

280,900 

148,877,000 

23.0217289 

8.0926723 

.001886792 

531 

281,961 

149,721,291 

23.0434372 

8.0977589 

.001883239 

532 

283,024 

150,568,768 

23.0651252 

8.1028390 

.001879699 

533 

284,089 

151,419,437 

23.0867928 

8.1079128 

.001876173 

534 

285,156 

152,273,304 

23.1084400 

8.1129803 

.001872659 

535 

286,225 

153,130,375 

23.1300670 

8.1180414 

.001869159 

536 

287,296 

153,990,656 

23.1516738 

8.1230962 

.001865672 

537 

288,369 

154,854,153 

23.1732605 

8.1281447 

.001862197 

538 

289,444 

155,720,872 

23.1948270 

8.1331870 

.001858736 

539 

290,521 

156,590,819 

23.2163735 

8.1382230 

.001855288 

540 

291,600 

157,464,000 

23.2379001 

8.1432529 

.001851852 

541 

292,681 

158,340,421 

23.2594067 

8.1482765 

.001848429 

542 

293,764 

159,220,088 

23.2808935 

8.1532939 

.001845018 

543 

294,849 

160,103,007 

23.3023604 

8.1583051 

.001841621 

544 

295,936 

160,989,184 

23.3238076 

8.1633102 

.001838235 

545 

297,025 

161,878,625 

23.3452351 

8.1683092 

.001834862 

546 

298,116 

162,771,336 

23.3666429 

8.1733020 

.001831502 

547 

299,209 

163,667,323 

23.3880311 

8.1782888 

.001828154 

548 

300,304 

164,566,592 

23.4093998 

8.1832695 

.001824818 

549 

301,401 

165,469,149 

23.4307490 

8.1882441 

.001821494 

550 

302,500 

166,375,000 

23  .  4520788 

8.1932127 

.001818182 

MISCELLANEOUS   TABLES   AND   DATA 


303 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

2V2 

N* 

#* 

N* 

l 

N 

551 

303,601 

167,284,151 

23.4733892 

8.1981753 

.001814882 

552 

304,704 

168,196,608 

23.4946802 

8.2031319 

.001811594 

553 

305,809 

169,112,377 

23.5159520 

8.2080825 

.001808318 

554 

306,916 

170,031,464 

23.5372046 

8.2130271 

.001805054 

555 

308,025 

170,953,875 

23.5584380 

8.2179657 

.001801802 

556 

309,136 

171,879,616 

23.5796522 

8.2228985 

.001798561 

557 

310,249 

172,808,693 

23.6008474 

8.2278254 

.001795332 

558 

311,364 

173,741,112 

23.6220236 

8.2327463 

.001792115 

559 

312,481 

174,676,879 

23.6431808 

8.2376614 

.001788909 

560 

313,600 

175,616,000 

23.6643191 

8.2425706 

.001785714 

561 

314,721 

176,558,481 

23.6854386 

8.2474740 

.001782531 

562 

315,844 

177,504,328 

23.7065392 

8.2523715 

.001779359 

563 

316,969 

178,453,547 

23.7276210 

8.2572633 

.001776199 

564 

318,096 

179,406,144 

23.7486842 

8.2621492 

.001773050 

565 

319,225 

180,362,125 

23.7697286 

8.2670294 

.001769912 

566 

320,356 

181,321,496 

23.7907545 

8.2719039 

.001766784 

567 

321,489 

182,284,263 

23.8117618 

8.2767726 

.001763668 

568 

322,624 

183,250,432 

23.8327506 

8.2816355 

.001760563 

569 

323,761 

184,220,009 

23.8537209 

8.2864928 

.001757469 

570 

324,900 

185,193,000 

23.8746728 

8.2913444 

.001754386 

571 

326,041 

186,169,411 

23.8956063 

8.2961903 

.001751313 

572 

327,184 

187,149,248 

23.9165215 

8.3010304 

.001748252 

573 

328,329 

188,132,517 

23.9374184 

8.3058651 

.001745201 

574 

329,476 

189,119,224 

23.9582971 

8.3106941 

.001742160 

575 

330,625 

190,109,375 

23.9791576 

8.3155175 

.001739130 

576 

331,776 

191,102,976 

24.0000000 

8.3203353 

.001736111 

577 

332,929 

192,100,033 

24.0208243 

8.3251475 

.001733102 

578 

334,084 

193,100,552 

24.0416306 

8.3299542 

.001730104 

579 

335,241 

194,104,539 

24.0624188 

8.3347553 

.001727116 

580 

336,400 

195,112,000 

24.0831891 

8.3395509 

.001724138 

581 

337,561 

196,122,941 

24.1039416 

8.3443410 

.001721170 

582 

338,724 

197,137,368 

24.1246762 

8.3491256 

.001718213 

583 

339,889 

198,155,287 

24.1453929 

8.3539047 

.001715266 

584 

341,056 

199,176,704 

24.1660919 

8.3586784 

.001712329 

585 

342,225 

200,201,625 

24.1867732 

8.3634466 

.001709402 

586 

343,396 

201,230,056 

24.2074369 

8.3682095 

.001706485 

587 

344,569 

202,262,003 

24.2280829 

8.3729668 

.001703578 

588 

345,744 

203,297,472 

24.2487113 

8.3777188 

.001700680 

589 

346,921 

204,336,469 

24.2693222 

8.3824653 

.001697793 

590 

348,100 

205,379,000 

24.2899156 

8.3872065 

.001694915 

591 

349,281 

206,425,071 

24.3104916 

8.3919423 

.001692047 

592 

350,464 

207,474,688 

24.3310501 

8.3966729 

.001689189 

593 

351,649 

208,527,857 

24.3515913 

8.4013981 

.001686341 

594 

352,836 

209,584,584 

24.3721152 

8.4061180 

.001683502 

595 

354,025 

210,644,875 

24.3926218 

8.4108326 

.001680672 

596 

355,216 

211,708,736 

24.4131112 

8.4155419 

.001677852 

597 

356,409 

212,776,173 

24.4335834 

8.4202460 

.001675042 

598 

357,604 

213,847,192 

24.4540385 

8.4249448 

.001672241 

599 

358,801 

214,921,799 

24.4744765 

8.4296383 

.001669449 

600 

360,000 

216,000,000 

24.4948974 

8.4343267 

.001666667 

304 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE   65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

2V2 

N*           N* 

N* 

1 
tT~ 

601 

361,201 

217,081,801 

24.5153013 

8.4390098 

.001663894 

602 

362,404 

218,167,208 

24.5356883 

8.4436877 

.001661130 

603 

363,609 

219,256,227 

24.5560583 

8.4483605 

.001658375 

604 

364,816 

220,348,864 

24.5764115 

8.4530281 

.001-655629 

605 

366,025 

221,445,125 

24.5967478 

8.4576906 

.001652893 

606 

367,236 

222,545,016 

24.6170673 

8.4623479 

.001650165 

607 

368,449 

223,648,543 

24.6373700 

8.4670001 

.001647446 

608 

369,664 

224,755,712 

24.6576560 

8.4716471 

.001644737 

609 

370,881 

225,866,529 

24.6779254 

8.4762892 

.001642036 

610 

372,100 

226,981,000 

24.6981781 

8.4809261 

.001639344 

611 

373,321 

228,099,131 

24.7184142 

8.4855579 

.001636661 

612 

374,544 

229,220,928 

24.7386338 

8.4901848 

.001633987 

613 

375,769 

230,346,397 

24.7588368 

8.4948065 

.001631321 

614 

376,996 

231,475,544 

24.7790234 

8.4994233 

.001628664 

615 

378,225 

232,608,375 

24.7991935 

8.5040350 

.001626016 

616 

379,456 

233,744,896 

24.8193473 

8.5086417 

.001623377 

617 

380,689 

234,885,113 

24.8394847 

8.5132435 

.001620746 

618 

381,924 

236,029,032 

24.8596058 

8.5178403 

.001618123 

619 

383,161 

237,176,659 

24.8797106 

8.5224321 

.001615509 

620 

384,400 

238,328,000 

24.8997992 

8.5270189 

.001612903 

621 

385,641 

239,483,061 

24.9198716 

8.5316009 

.001610306 

622 

386,884 

240,641,848 

24.9399278 

8.5361780 

.001607717 

623 

388,129 

241,804,367 

24.9599679 

8.5407501 

.001605136 

624 

389,376 

242,970,624 

24.9799920 

8.5453173 

.001602564 

625 

390,625 

244,140,625 

25.0000000 

8.5498797 

.001600000 

626 

391,876 

245,314,376 

25.0199920 

8.5544372 

.001597444 

627 

393,129 

246,491,883 

25.0399681 

8.5589899 

.001594896 

628 

394,384 

247,573,152 

25.0599282 

8.5635377 

.001592357 

629 

395,641 

248,858,189 

25.0798724 

8.5680807 

.001589825 

630 

396,900 

250,047,000 

25.0998008 

8.5726189 

.001587302 

631 

398,161 

251,239,591 

25.1197134 

8.5771523 

.001584786 

632 

399,424 

252,435,968 

25.1396102 

8.5816809 

.001582278 

633 

400,689 

253,636,137 

25.1594913 

8.5862047 

.001579779 

634 

401,956 

254,840,104 

25.1793566 

8.5907238 

.001577287 

635 

403,225 

256,047,875 

25.1992063 

8.5952380 

.001574803 

636 

404,496 

257,259,456 

25.2190404 

8.5997476 

.001572327 

637 

405,769 

258,474,853 

25.2388589 

8.6042525 

.001569859 

638 

407,044 

259,694,072 

25.2586619 

8.6087526 

.001567398 

639 

408,321 

260,917,119 

25.2784493 

8.6132480 

.001564945 

640 

409,600 

262,144,000 

25.2982213 

8.6177388 

.001562500 

641 

410,881 

263,374,721 

25.3179778 

8.6222248 

.001560062 

642 

412,164 

264,609,288 

25.3377189 

8.6267063 

.001557632 

643 

413,449 

265,847,707 

25.3574447 

8.6311830 

.001555210 

644 

414,736 

267,089,984 

25.3771551 

8.6356551 

.001552795 

645 

416,025 

268,336,125 

25.3968502 

8.6401226 

.001550388 

646 

417,316 

269,586,136 

25.4165301 

8.6445855 

.001547988 

647 

418,609 

270,840,023 

25.4361947 

8.6490437 

.001545595 

648 

419,904 

272,097,792 

25.4558441 

8.6534974 

.001543210 

649 

421,201 

273,359,449 

25.4754784 

8.6579465 

.001540832 

650 

422,500 

274,625,000 

25.4950976 

8.6623911 

.001538462 

MISCELLANEOUS   TABLES   AND   DATA 


305 


TABLE   65  (Continued] 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

AT2 

N* 

N* 

N* 

l 
AT 

651 

423,801 

275,894,451 

25.5147016 

8.6668310 

.001536098 

652 

425,104 

277,167,808 

25.5342907 

8.6712665 

.001533742 

653 

426,409 

278,445,077 

25.5538647 

8.6756974 

.001531394 

654 

427,716 

279,726,264 

25.5734237 

8.6801237 

.001529052 

655 

429,025 

281,011,375 

25.5929678 

8.6845456 

.001526718 

656 

430,336 

282,300,416 

25.6124969 

8.6889630 

.001524390 

657 

431,649 

283,593,393 

25.6320112 

8.6933759 

.001522070 

658 

432,964 

284,890,312 

25.6515107 

8.6977843 

.001519757 

659 

434,281 

286,191,179 

25.6709953 

8.7021882 

.001517451 

660 

435,600 

287,496,000 

25.6904652 

8.7065877 

.001515152 

661 

436,921 

288,804,781 

25.7099203 

8.7109827 

.001512859 

662 

438,244 

290,117,528 

25.7293607 

8.7153734 

.001510574 

663 

439,569 

291,434,247 

25.7487864 

8.7197596 

.001508296 

664 

440,896 

292,754,944 

25.7681975 

8.7241414 

.001506024 

665 

442,225 

294,079,625 

25.7875939 

8.7285187 

.001503759 

666 

443,556 

295,408,296 

25.8069758 

8.7328918 

.001501502 

667 

444,889 

296,740,963 

25.8263431 

8.7372604 

.001499250 

668 

446,224 

298,077,632 

25.8456960 

8.7416246 

.001497006 

669 

447,561 

299,418,309 

25.8650343 

8.7459846 

.001494768 

670 

448,900 

300,763,000 

25.8843582' 

8.7503401 

.001492537 

671 

450,241 

302,111,711 

25.9036677 

8.7546913 

.001490313 

672 

451,584 

303,464,448 

25.9229628 

8.7590383 

.001488095 

673 

452,929 

304,821,217 

25.9422435 

8.7633809 

.001485884 

674 

454,276 

306,192,024 

25.9615100 

8.7677192 

.001483680 

675 

455,625 

307,546,875 

25.9807621 

8.7720532 

.001481481 

676 

456,976 

308,915,776 

26.0000000 

8.7763830 

.001479290 

677 

458,329 

310,288,733 

26.0192237 

8.7807084 

.001477105 

678 

459,684 

311,665,752 

26.0384331 

8.7850296 

.001474926 

679 

461,041 

313,046,839 

26.0576284 

8.7893466 

.001472754 

680 

462,400 

314,432,000 

26.0768096 

8.7936593 

.001470588 

681 

463,761 

315,821,241 

26.0959767 

8.7979679 

.001468429 

682 

465,124 

317,214,568 

26.1151297 

8.8022721 

.001466276 

683 

466,489 

318,611,987 

26.1342687 

8.8065722  - 

.001464129 

684 

467,856 

320,013,504 

26.1533937 

8.8108681 

.001461988 

685 

469,225 

321,419,125 

26.1725047 

8.8151598 

.001459854 

686 

470,596 

322,828,856 

26.1916017 

8.8194474 

.001457726 

687 

471,969 

324,242,703 

26.2106848 

8.8237307 

.001455604 

688 

473,344 

325,660,672 

26.2297541 

8.8280099 

.001453488 

689 

474,721 

327,082,769 

26.2488095 

8.8322850 

.001451379 

690 

476,100 

328,509,000 

26.2678511 

8.8365559 

.001449275 

691 

477,481 

329,939,371 

26.2868789 

8.8408227 

.001447178 

692 

478,864 

331,373,888 

26.3058929 

8.8450854 

.001445087 

693 

480,249 

332,812,557 

26.3248932 

8.8493440 

.001443001 

694 

481,636 

334,255,384 

26.3438797 

8.8535985 

.001440922 

695 

483,025 

335,702,375 

26.3628527 

8.8578489 

.001438849 

696 

484,416 

337,153,536 

26.3818119 

8.8620952 

.001436782 

697 

485,809 

338,608,873 

26.4007576 

8.8663375 

.001434720 

698 

487,204 

340,068,392 

26.4196896 

8.8705757 

.001432665 

699 

488,601 

341,532,099 

26.4386081 

8.8748099 

.001430615 

700 

490,000 

343,000,000 

26.4575131 

8.8790400 

.001428571 

306 


WORKING  DATA  FOR   IRRIGATION   ENGINEERS 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

W* 

N3 

N* 

*i 

1 

"  N 

701 

491,401 

344,472,101 

26.4764046 

8.8832661 

.001426534 

702 

492,804 

345,948,408 

26.4952826 

8.8874882 

.001424501 

703 

494,209 

347,428,927 

26.5141472 

8.8917063 

.001422475 

704 

495,616 

348,913,664 

26.5329983 

8.8959204 

.001420455 

705 

497,025 

350,402,625 

26.5518361 

8.9001304 

.001418440 

706 

498,436 

351,895,816 

26.5706605 

8.9043366 

.001416431 

707 

499,849 

353,393,243 

26.5894716 

8.9085387 

.001414427 

708 

501,264 

354,894,912 

26.6082694 

8.9127369 

.001412429 

709 

502,681 

356,400,829 

26.6270539 

8.9169311 

.001410437 

710 

504,100 

357,911,000 

26.6458252 

8.9211214 

.001408451 

711 

505,521 

359,425,431 

26.6645833 

8.9253078 

.001406470 

712 

506,944 

360,944,128 

26.6833281 

8.9294902 

.001404494 

713 

508,369 

362,467,097 

26.7020598 

8.9336687 

.001402525 

714 

509,796 

363,994,344 

26.7207784 

8.9378433 

.001400560 

715 

511,225 

365,525,875 

26.7394839 

8.9420140 

.001398601 

716 

512,656 

367,061,696 

26.7581763 

8.9461809 

.001396648 

717 

514,089 

368,601,813 

26.7768557 

8.9503438 

.001394700 

718 

515,524 

370,146,232 

26.7955220 

8.9545029 

.001392758 

719 

516,961 

371,694,959 

26.8141754 

8.9586581 

.001390821 

720 

518,400 

373,248,000 

26.8328157 

8.9628095 

.001388889 

721 

519,841 

374,805,361 

26.8514432 

8.9669570 

.001386963 

722 

521,284 

376,367,048 

26.8700577 

8.9711007 

.001385042 

723 

522,729 

377,933,067 

26.8886593 

8.9752406 

.001383126 

724 

524,176 

379,503,424 

26.9072481 

8.9793766 

.001381215 

725 

525,625 

381,078,125 

26.9258240 

8.9835089 

.001379310 

726 

527,076 

382,657,176 

26.9443872 

8.9876373 

.001377410 

727 

528,529 

384,240,583 

26.9629375 

8.9917620 

.001375516 

728 

529,984 

385,828,352 

26.9814751 

8.9958829 

.001373626 

729 

531,441 

387,420,489 

27.0000000 

9.0000000 

.001371742 

730 

532,900 

389,017,000 

27.0185122 

9.0041134 

.001369863 

731 

534,361 

390,617,891 

27.0370117 

9.0082229 

.001367989 

732 

535,824 

392,223,168 

27.0554985 

9.0123288 

.001366120 

733 

537,289 

393,832,837 

27.0739727 

9.0164309 

.001364256 

734 

538,756 

395,446,904 

27.0924344 

9.0205293 

.001362398 

735 

540,225 

397,065,375 

27.1108834 

9.0246239 

.001360544 

736 

541,696 

398,688,256 

27.1293199 

9.0287149 

.001358696 

737 

543,169 

400,315,553 

27.1477439 

9.0328021 

.001356852 

738 

544,644 

401,947,272 

27.1661554 

9.0368857 

.001355014 

739 

546,121 

403,583,419 

27.1845544 

9.0409655 

.001353180 

740 

547,600 

405,224,000 

27.2029410 

9.0450417 

.001351351 

741 

549,081 

406,869,021 

27.2213152 

9.0491142 

.001349528 

742 

550,564 

408,518,488 

27.2396769 

9.0531831 

.001347709 

743 

552,049 

410,172,407 

27.2580263 

9.0572482 

.001345895 

744 

553,536 

411,830,784 

27.2763634 

9.0613098 

.001344086 

745 

555,025 

413,493,625 

27.2946881 

9.0653677 

.001342282 

746 

556,516 

415,160,936 

27.3130006 

9.0694220 

.001340483 

747 

558,009 

416,832,723 

27.3313007 

9.0734726 

.001338688 

748 

559,504 

418,508,992 

27.3495887 

9.0775197 

.001336898 

749 

561,001 

420,189,749 

27.3678644 

9.0815631 

.001335113 

750 

562,500 

421,875,000 

27.3861279 

9.0856030 

.001333333 

MISCELLANEOUS   TABLES  AND  DATA 


307 


TABLE  65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

y* 

N^ 

N* 

N* 

1 

N 

751 

564,001 

423,564,751 

27.4043792 

9.0896392 

.001331558 

752 

565,504 

425,259,008 

27.4226184 

9.0936719 

.001329787 

753 

567,009 

426,957,777 

27.4408455 

9.0977010 

.001328021 

754 

568,516 

428,661,064 

27.4590604 

9.1017265 

.001326260 

755 

570,025 

430,368,875 

27.4772633 

9.1057485 

.001324503 

756 

571,536 

432,081,216 

27.4954542 

9.1097669 

.001322751 

757 

573,049 

433,798,093 

27.5136330 

9.1137818 

.001321004 

758 

574,564 

435,519,512 

27.5317998 

9.1177931 

.001319261 

759 

576,081 

437,245,479 

27.5499546 

9.1218010 

.001317523 

760 

577,600 

438,976,000 

27.5680975 

9.1258053 

.001315789 

761 

579,121 

440,711,081 

27.5862284 

9.1298061 

.001314060 

762 

580,644 

442,450,728 

27.6043475 

9.1338034 

.001312336 

763 

582,169 

444,194,947 

27.6224546 

9.1377971 

.001310616 

764 

583,696 

445,943,744 

27.6405499 

9.1417874 

.001308901 

765 

585,225 

447,697,125 

27.6586334 

9.1457742 

.001307190 

766 

586,756 

449,455,096 

27.6767050 

9.1497576 

.001305483 

767 

588,289 

451,217,663 

27.6947648 

9.1537375 

.001303781 

768 

589,824 

452,984,832 

27.7128129 

9.1577139 

.001302083 

769 

591,361 

454,756,609 

27.7308492 

9.1616869 

.001300390 

770 

592,900 

456,533,000 

27.7488739 

9.1656565 

.001298701 

771 

594,441 

458,314,011 

27.7668868 

9.1696225 

.001297017 

772 

595,984 

460,099,648 

27.7848880 

9.1735852 

.001295337 

773 

597,529 

461,889,917 

27.8028775 

9.1775445 

.001293661 

774 

599,076 

463,684,824 

27.8208555 

9.1815003 

.001291990 

775 

600,625 

465,484,375 

27.8388218 

9.1854527 

.001290323 

776 

602,176 

467,288,576 

27.8567766 

9.1894018 

.001288660 

777 

603,729 

469,097,433 

27.8747197 

9.1933474 

.001287001 

778 

605,284 

470,910,952 

27.8926514 

9.1972897 

.001285347 

779 

606,841 

472,729,139 

27.9105715 

9.2012286 

.001283697 

780 

608,400 

474,552,000 

27.9284801 

9.2051641 

.001282051 

781 

609,961 

476,379,541 

27.9463772 

9.2090962 

.001280410 

782 

611,524 

478,211,768 

27.9642629 

9.2130250 

.001278772 

783 

613,089 

480,048,687 

27.9821372 

9.2169505 

.001277139 

784 

614,656 

481,890,304 

28.0000000 

9.2208726 

.001275510 

785 

616,225 

483,736,625 

28.0178515 

9.2247914 

.001273885 

786 

617,796 

485,587,656 

28.0356915 

9.2287068 

.001272265 

787 

619,369 

487,443,403 

28.0535203 

9.2326189 

.001270648 

788 

620,944 

489,303,872 

28.0713377 

9.2365277 

.001269036 

789 

622,521 

491,169,069 

28.0891438 

9.2404333 

.001267427 

790 

624,100 

493.039,000 

28.1069386 

9.2443355 

.00126-5823 

791 

625,681 

494,913,671 

28.1247222 

9.2482344 

.001264223 

792 

627,264 

496,793,088 

28.1424946 

9.2521300 

.001262626 

793 

628,849 

498,677,257 

28.1602557 

9.2560224 

.001261034 

794 

630,436 

500,566,184 

28.1780056 

9.2599114 

.001259446 

795 

632,025 

502,459,875 

28.1957444 

9.2637973 

.001257862 

796 

633,616 

504,358,336 

28.2134720 

9.2676798 

.001256281 

797 

635,209 

506,261,573 

28.2311884 

9.2715592 

.001254705 

798 

636,804 

508,169,592 

28.2488938 

9.2754352 

.001253133 

799 

638,401 

510,082,399 

28.2665881 

9.2793081 

.001251564 

800 

640,000 

512,000,000 

28.2842712 

9.2831777 

.001250000 

308 


WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


TABLE   65  (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

7\T2 

#3 

N* 

N* 

1 

is 

801 

641,601 

513,922,401 

28.3019434 

9.2870440 

.001248439 

802 

643,204 

515,849,608 

28.3196045 

9.2909072 

.001246883 

803 

644,809 

517,781,627 

28.3372546 

9.2947671 

.001245330 

804 

646,416 

519,718,464 

28.3548938 

9.2986239 

.001243781 

805 

648,025 

521,660,125 

28.3725219 

9.3024775 

.001242236 

806 

649,636 

523,606,616 

28.3901391 

9.3063278 

.001240695 

807 

651,249 

525,557,943 

28.4077454 

9.3101750 

.001239157 

808 

652,864 

527,514,112 

28.4253408 

9.3140190 

.001237624 

809 

654,481 

529,475,129 

28.4429253 

9.3178599 

.001236094 

810 

656,100 

531,441,000 

28.4604989 

9.3216975 

.001234568 

811 

657,721 

533,411,731 

28.4780617 

9.3255320 

.001233046 

812 

659,344 

535,387,328 

28.4956137 

9.3293634 

.001231527 

813 

660,969 

537,367,797 

28.5131549 

9.3331916 

.001230012 

814 

662,596 

539,353,144 

28.5306852 

9.3370167 

.001228501 

815 

664,225 

541,343,375 

28.5482048 

9.3408386 

.001226994 

816 

665,856 

543,338,496 

28.5657137 

9.3446575 

.001225490 

817 

667,489 

545,338,513 

28.5832119 

9.3484731 

.001223990 

818 

669,124 

547,343,432 

28.6006993 

9.3522857 

.001222494 

819 

670,761 

549,353,259 

28.6181760 

9.3560952 

.001221001 

820 

672,400 

551,368,000 

28.6356421 

9.3599016 

.001219512 

821 

674,041 

553,387,661 

28.6530976 

9.3637049 

.001218027 

822 

675,684 

555,412,248 

28.6705424 

9.3675051 

.001216545 

823 

677,329 

557,441,767 

28.6879766 

9.3713022 

.001215067 

824 

678,976 

559,476,224 

28.7054002 

9.3750963 

.001213592 

825 

680,625 

561,515,625 

28.7228132 

9.3788873 

.001212121 

826 

682,276 

563,559,976 

28.7402157 

9.3826752 

.001210654 

827 

683,929 

565,609,283 

28.7576077 

9.3864600 

.001209190 

828 

685,584 

567,663,552 

28.7749891 

9.3902419 

.001207729 

829 

687,241 

569,722,789 

28.7923601 

9.3940206 

.001206273 

830 

688,900 

571,787,000 

28.8097206 

9.3977964 

.001204819 

831 

690,561 

573,856,191 

28.8270706 

9.4015691 

.001203369 

832 

692,224 

575,930,368 

28.8444102 

9.4053387 

.001201923 

833 

693,889 

578,009,537 

28.8617394 

9.4091054 

.001200480 

834 

695,556 

580,093,704 

28.8790582 

9.4128690 

.001199041 

835 

697,225 

582,182,875 

28.8963666 

9.4166297 

.001197605 

836 

698,896 

584,277,056 

28.9136646 

9.4203873 

.001196172 

837 

700,569 

586,376,253 

28.9309523 

9.4241420 

.001194743 

838 

702,244 

588,480,472 

28.9482297 

9.4278936 

.001193317 

839 

703,921 

590,589,719 

28.9654967 

9.4316423 

.001191895 

840 

705,600 

592,704,000 

28.9827535 

9.4353880 

.001190476 

841 

707,281 

594,823,321 

29.0000000 

9.4391307 

.001189061 

842 

708,964 

596,947,688 

29.0172363 

9.4428704 

.001187648 

843 

710,649 

599,077,107 

29.0344623 

9.4466072 

.001186240 

844 

712,336 

601,211,584 

29.0516781 

9.4503410 

.001184834 

845 

714,025 

603,351,125 

29.0688837 

9.4540719 

.001183432 

846 

715,716 

605,495,736 

29.0860791 

9.4577999 

.001182033 

847 

717,409 

607,645,423 

29.1032644 

9.4615249 

.001180638 

848 

719,104 

609,800,192 

29.1204396 

9.4652470 

.001179245 

849 

720,801 

611,960,049 

29.1376046 

9.4689661 

.001177856 

850 

722,500 

614,125,000 

29.1547595 

9.4726824 

.001176471 

MISCELLANEOUS  TABLES  AND  DATA 


309 


TABLE   65  (Continued} 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

N* 

^3 

N* 

N* 

1 
N 

851 

724,201 

616,295,051 

29.1719043 

9.4763957 

.001175088 

852 

725,904 

618,470,208 

29.1890390 

9.4801061 

.001173709 

853 

727,609 

620,650,477 

29.2061637 

9.4838136 

.001172333 

854 

729,316 

622,835,864 

29.2232784 

9.4875182 

.001170960 

855 

731,025 

625,026,375 

29.2403830 

9.4912200 

.001169591 

856 

732,736 

627,222,016 

29.2574777 

9.4949188 

.001168224 

857 

734,449 

629,422,793 

29.2745623 

9.4986147 

.001166861 

858 

736,164 

631,628,712 

29.2916370 

9.5023078 

.001165501 

859 

737,881 

633,839,779 

29.3087018 

9.5059980 

.001164144 

860 

739,600 

636,056,000 

29.3257566 

9.5096854 

.001162791 

861 

741,321 

638,277,381 

29.3428015 

9.5133699 

.001161440 

862 

743,044 

640,503,928 

29.3598365 

9.5170515 

.001160093 

863 

744,769 

642,735,647 

29.3768616 

9.5207303 

.001158749 

864 

746,496 

644,972,544 

29.3938769 

9.5244063 

.001157407 

865 

748,225 

647,214,625 

29.4108823 

9.5280794 

.001156069 

866 

749,956 

649,461,896 

29.4278779 

9.5317497 

.001154734 

867 

751,689 

651,714,363 

29.4448637 

9.5354172 

.001153403 

868 

753,424 

653,972,032 

29.4618397 

9.5390818 

.001152074 

869 

755,161 

656,234,909 

29.4788059 

9.5427437 

.001150748 

870 

756,900 

658,503,000 

29.4957624 

9.5464027 

.001149425 

871 

758,641 

660,776,311 

29.5127091 

9.5500589 

.001148106 

872 

760,384 

663,054,848 

29.5296461 

9.5537123 

.001146789 

873 

762,129 

665,338,617 

29.5465734 

9.5573630 

.001145475 

874 

763,876 

667,627,624 

29.5634910 

9.5610108 

.001144165 

875 

765,625 

669,921,875 

29.5803989 

9.5646559 

.001142857 

876 

767,376 

672,221,376 

29.5972972 

9.5682982 

.001141553 

877 

769,129 

674,526,133 

29.6141858 

9.5719377 

.001140251 

878 

770,884 

676,836,152 

29.6310648 

9.5755745 

.001138952 

879 

772,641 

679,151,439 

29.6479342 

9.5792085 

.001137656 

880 

774,400 

681,472,000 

29.6647939 

9.5828397 

.001136364 

881 

776,161 

683,797,841 

29.6816442 

9.5864682 

.001135074 

882 

777,924 

686,128,968 

29.6984848 

9.5900939 

.001133787 

883 

779,689 

688,465,387 

29.7153159 

9.5937169 

.001132503 

884 

781,456 

690,807,104 

29.7321375 

9.5973373 

.001131222 

885 

783,225 

693,154,125 

29.7489496 

9.6009548 

.001129944 

886 

784,996 

695,506,456 

29.7657521 

9.6045696 

.001128668 

887 

786,769 

697,864,103 

29.7825452 

9.6081817 

.001127396 

888 

788,544 

700,227,072 

29.7993289 

9.6117911 

.001126126 

889 

790,321 

702,595,369 

29.8161030 

9.6153977 

.001124859 

890 

792,100 

704,969,000 

29.8328678 

9.6190017 

.001123596 

891 

793,881 

707,347,971 

29.8496231 

9.6226030 

.001122334 

892 

795,664 

709,732,288 

29.8663690 

9.6262016 

.001121076 

893 

797,449 

712,121,957 

29.8831056 

9.6297975 

.001119821 

894 

799,236 

714,516,984 

29.8998328 

9.6333907 

.001118568 

895 

801,025 

716,917,375 

29.9165506 

9.6369812 

.001117318 

896 

802,816 

719,323,136 

29.9332591 

9.6405690 

.001116071 

897 

804,609 

721,734,273 

29.9499583 

9.6441542 

.001114827 

898 

806,404 

724,150,792 

29.9666481 

9.6477367 

.001113586 

899 

808,201 

726,572,699 

29.9833287 

9.6513166 

.001112347 

900 

810,000 

729,000,000 

30.0000000 

9.6548938 

.001111111 

310 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


TABLE  65   (Continued) 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

7V2 

N* 

N*    . 

*  1  4- 

901 

811,801 

731,432,701 

30.0166620 

9.6584684 

.001109878 

902 

813,604 

733,870,808 

30.0333148 

9.6620403 

.001108647 

903 

815,409 

736,314,327 

30.0499584 

9.6656096 

.001107420 

904 

817,216 

738,763,264 

30.0665928 

9.6691762 

.001106195 

905 

819,025 

741,217,625 

30.0832179 

9.6727403 

.001104972 

906 

820,836 

743,677,416 

30.0998339 

9.6763017 

.001103753 

907 

822,649 

746,142,643 

30.1164407 

9.6798604 

.001102536 

908 

824,464 

748,613,312 

30.1330383 

9.6834166 

.001101322 

909 

826,281 

751,089,429 

30.1496269 

9.6869701 

.001100110 

910 

828,100 

753,571,000 

30.1662063 

9.6905211 

.001098901 

911 

829,921 

756,058,031 

30.1827765 

9.6940694 

.001097695 

912 

831,744 

758,550,528 

30.1993377 

9.6976151 

.001096491 

913 

833,569 

761,048,497 

30.2158899 

9.7011583 

.001095290 

914 

835,396 

763,551,944 

30.2324329 

9.7046989 

.001094092 

915 

837,225 

766,060,875 

30.2489669 

9.7082369 

.001092896 

916 

839,056 

768,575,296 

30.2654919 

9.7117723 

.001091703 

917 

840,889 

771,095,213 

30.2820079 

9.7153051 

.001090513 

918 

842,724 

773,620,632 

30.2985148 

9.7188354 

.001089325 

919 

844,561 

776,151,559 

30.3150128 

9.7223631 

.001088139 

920 

846,400 

778,688,000 

30.3315018 

9.7258883 

.001086957 

921 

848,241 

781,229,961 

30.3479818 

9.7294109 

.001085776 

922 

850,084 

783,777,448 

30.3644529 

9.7329309 

.001084599 

923 

851,929 

786,330,467 

30.3809151 

9.7364484 

.001083424 

924 

853,776 

788,889,024 

30.3973683 

9.7399634 

.001082251 

925 

855,625 

791,453,125 

30.4138127 

9.7434758 

.001081081 

926 

857,476 

794,022,776 

30.4302481 

9.7469857 

.001079914 

927 

859,329 

796,597,983 

30.4466747 

9.7504930 

.001078749 

928 

861,184 

799,178,752 

30.4630924 

9.7539979 

.001077586 

929 

863,041 

801,765,089 

30.4795013 

9.7575002 

.001076426 

930 

864,900 

804,357,000 

30.4959014 

9.7610001 

.001075269 

931 

866,761 

806,954,491 

30.5122926 

9.7644974 

.001074114 

932 

868,624 

809,557,568 

30.5286750 

9.7679922 

.001072961 

933 

870,489 

812,166,237 

30.5450487 

9.7714845 

.001071811 

934 

872,356 

814,780,504 

30.5614136 

9.7749743 

.001070664 

935 

874,225 

817,400,375 

30.5777697 

9.7784616 

.001069519 

936 

876,096 

820,025,856 

30.5941171 

9.7819466 

.001068376 

937 

877,969 

822,656,953 

30.6104557 

9.7854288 

.001067236 

938 

879,844 

825,293,672 

30.6267857 

9.7889087 

.001066098 

939 

881,721 

827,936,019 

30.6431069 

9.7923861 

.001064963 

940 

883,600 

830,584,000 

30.6594194 

9.7958611 

.001063830 

941 

855,481 

833,237,621 

30.6757233 

9.7993336 

.001062699 

942 

887,364 

835,896,888 

30.6920185 

9.8028036 

.001061571 

943 

889,249 

838,561,807 

30.7083051 

9.8062711 

.001060445 

944 

891,136 

841,232,384 

30.7245830 

9.8097362 

.001059322 

945 

893,025 

843,908,625 

30.7408523 

9.8131989 

.001058201 

946 

894,916 

846,590,536 

30.7571130 

9.8166591 

.001057082 

947 

896,809 

849,278,123 

30.7733651 

9.8201169 

.001055966 

948 

898,704 

851,971,392 

30.7896086 

9.8235723 

.001054852 

949 

900,601 

854,670,349 

30.8058436 

9.8270252 

.001053741 

950 

902,500 

857,375,000 

30.8220700   9.8304757 

.001052632 

MISCELLANEOUS   TABLES   AND   DATA 


311 


TABLE  65  (Concluded] 
SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS,  RECIPROCALS 


N 

#2 

N* 

AT* 

^ 

l 
If 

951 

904,401 

860,085,351 

30.8382879 

9.8339238 

.001051525 

952 

906,304 

862,801,408 

30.8544972 

9.8373695 

.001050420 

953 

908,209 

865,523,177 

30.8706981 

9.8408127 

.001049318 

954 

910,116 

868,250,664 

30.8868904 

9.8442536 

.001048218 

955 

912,025 

870,983,875 

30.9030743 

9.8476920 

.001047120 

956 

913,936 

873,722,816 

30.9192497 

9.8511280 

.001046025 

957 

915,849 

876,467,493 

30.9354166 

9.8545617 

.001044932 

958 

917,764 

879,217,912 

30.9515751 

9.8579929 

.001043841 

959 

919,681 

881,974,079 

30.9677251 

9.8614218 

.001042753 

960 

921,600 

884,736,000 

30.9838668 

9.8648483 

.001041667 

961 

923,521 

887,503,681 

31.0000000 

9.8682724 

.001040583 

962 

925,444 

890,277,128 

31.0161248 

9.8716941 

.001039501 

963 

927,369 

893,056,347 

31.0322413 

9.8751135 

.001038422 

964 

929,296 

895,841,344 

31.0483494 

9.8785305 

.001037344 

965 

931,225 

898,632,125 

31.0644491 

9.8819451 

.001036269 

966 

933,156 

901,428,696 

31.0805405 

9.8853574 

.001035197 

967 

935,089 

904,231,063 

31.0966236 

9.8887673 

.001034126 

968 

937,024 

907,039,232 

31.1126984 

9.8921749 

.001033058 

969 

938,961 

909,853,209 

31.1287648 

9.8955801 

.001031992 

970 

940,900 

912,673,000 

31.1448230 

9.8989830 

.001030928 

971 

942,841 

915,498,611 

31.1608729 

9.9023835 

.001029866 

972 

944,784 

918,330,048 

31  .  1769145 

9.9057817 

.001028807 

973 

946,729 

921,167,317 

31.1929479 

9.9091776 

.001027749 

974 

948,676 

924,010,424 

31.2089731 

9.9125712 

.001026694 

975 

950,625 

926,859,375 

31.2249900 

9.9159624 

.001025641 

976 

952,576 

929,714,176 

31.2409987 

9.9193513 

.001024590 

977 

954,529 

932,574,833 

31.2569992 

9.9227379 

.001023541 

978 

956,484 

935,441,352 

31.2729915 

9.9261222 

.001022495 

979 

958,441 

938,313,739 

31.2889757 

9.9295042 

.001021450 

980 

960,400 

941,192,000 

31.3049517 

9.9328839 

.001020408 

981 

962,361 

944,076,141 

31.3209195 

9.9362613 

.001019368 

982 

964,324 

946,966,168 

31.3368792 

9.9396363 

.001018330 

983 

966,289 

949,862,087 

31.3528308 

9.9430092 

.001017294 

984 

968,256 

952,763,904 

31.3687743 

9.9463797 

.001016260 

985 

970,225 

955,671,625 

31.3847097 

9.9497479 

.001015228 

986 

972,196 

958,585,256 

31.4006369 

9.9531138 

.001014199 

987 

974,169 

961,504,803 

31.4165561 

9.9564775 

.001013171 

988 

976,144 

964,430,272 

31.4324673 

9.9598389 

.001012146 

989 

978,121 

967,361,669 

31.4483704 

9.9631981 

.001011122 

990 

980,100 

970,299,000 

31.4642654 

9.9665549 

.001010101 

991 

982,081 

973,242,271 

31.4801525 

9.9699095 

.001009082 

992 

984,064 

976,191,488 

31.4960315 

9.9732619 

.001008065 

993 

986,049 

979,146,657 

31.5119025 

9.9766120 

.001007049 

994 

988,036 

982,107,784 

31.5277655 

9.9799599 

.001006036 

995 

990,025 

985,074,875 

31.5436206 

9.9833055 

.001005025 

996 

992,016 

988,047,936 

31.5594677 

9.9866488 

.001004016 

997 

994,009 

991,026,973 

31.5753068 

9.9899900 

.001003009 

998 

996,004 

994,011,992 

31.5911380 

9.9933289 

.001002004 

999 

998,001 

997,002,999 

31.6069613 

9.9966656 

.001001001 

1000 

1,000,000  1,000,000,000 

31.6227766 

10.0000000 

.001000000 

CHAPTER  VII 
SPECIFICATIONS 


CHAPTER  VII 
SPECIFICATIONS 

SPECIFICATIONS  are  a  definite,  particularized,  and  complete 
statement  of  the  legal  and  engineering  or  technical  requirements 
to  be  met  in  performing  the  work  covered  thereby. 

The  importance  of  having  a  clear,  concise,  and  definite  set  of 
specifications  is  frequently  minimized,  especially  by  engineers 
who  have  not  had  extensive  experience  in  carrying  out  important 
works.  Even  engineers  of  large  experience  sometimes  minimize 
this  important  requirement  because  they  may  have  been  for- 
tunate enough  to  carry  through  their  work  with  less  extensive 
and  detail  specifications,  but  it  is  probably  safe  to  say  that  the 
importance  of  the  latter  sooner  or  later  becomes  evident. 

In  general,  specifications,  except  as  to  the  legal  requirements, 
should  not  be  intended  as  a  rigid  set  of  rules  to  be  scrupulously 
followed  according  to  the  letter,  but  as  a  guide  to  indicate  to 
the  contractor  the  quantity  and  quality  of  the  work  that  the 
engineer  will  require  him  to  do.  The  language  must,  therefore, 
be  definite  and  clear,  so  as  to  be  susceptible  of  only  one  inter- 
pretation. This  protects  both  the  contractor  and  the  engineer, 
for,  if  the  contractor  bids  too  low  because  of  a  misinterpreta- 
tion of  the  engineer's  requirements,  he  either  loses  money  or  the 
engineer  must  allow  him  additional  compensation  above  the 
contract  price.  In  either  case,  friction  and  bad  feeling  may 
ensue  with  resulting  detriment  to  the  work. 

The  specifications  of  the  United  States  Reclamation  Service, 
which  have  been  gradually  evolved  during  a  period  of  twelve 
years'  construction  of  important  irrigation  works,  may  well  be 
taken  as  a  model  by  irrigation  engineers.  Some  of  these 
specifications  that  have  become  more  or  less  standardized  are 
printed  in  the  following  pages,  with  some  modifications. 

The  specifications  given  are  not  intended  to  be  used  without 
modification.  There  might  be  cases  where  they  could  be  so 
used,  but  the  main  intention  is  to  state  the  important  points  to 

315 


316  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

be  covered  rather  than  to  state  how  they  should  be  covered. 
With  this  information  at  hand  it  becomes  a  comparatively  simple 
matter  to  draw  up  specifications  adaptable  to  the  peculiar  local 
conditions  involved,  whereas,  without  such  information,  impor- 
tant clauses  are  very  liable  to  be  overlooked. 

Subdivisions  of  Specifications. — A  complete  set  of  specifica- 
tions consists  of  the  following: 

1.  The  advertisement. 

2.  Notice  to  bidders. 

3.  The  proposal. 

4.  Guarantee  of  bond. 

5.  Statement  of  work  to  be  performed. 

6.  General  conditions,  legal  requirements,  etc. 

7.  Detailed  specifications. 

8.  Drawings. 

THE  ADVERTISEMENT 

For  public  work  (Federal,  State,  Municipal,  etc.),  advertising 
is  usually  required  by  law.  Private  work  may  or  may  not  be 
advertised  publicly.  In  any  case,  the  value  of  wide  publicity  is 
evident,  as  by  this  means  the  greatest  competition  is  obtained. 
The  advertisement  should  state  clearly,  concisely,  and  briefly 
when  and  where  bids  will  be  received,  what  the  work  is  that  is 
to  be  performed,  the  approximate  quantities  involved,  where  the 
work  is  located,  and  from  whom  particulars  may  be  obtained. 
A  form  commonly  used  by  the  Reclamation  Service  is  as  follows: 

"  Washington,  D.  C., ,  19. . 

"  Sealed  proposals  will  be  received  at  the  office  of  the  United 

States  Reclamation  Service  at until  2   o'clock  P.M., 

,  19. . . ,  for  canal  excavation  and  structures,  involv- 
ing about cubic  yards  of  excavation, cubic 

yards  of  reinforced  concrete,  etc.,  etc.    The  work  is  situated 

"  For  particulars,  address  the  United  States  Reclamation 
Service, 

"(sgd.)   .',.;.;: " 


SPECIFICATIONS  317 


NOTICE  TO  BIDDERS 

This  should  be  placed  in  a  conspicuous  place  at  the  beginning 
of  the  specifications.  The  purpose  of  this  "  notice  "  is  to  call 
particularly  to  the  attention  of  bidders  such  requirements  as 
they  should  take  special  cognizance  of  before  preparing  their 
bids,  such  as  the  requirement  for  certified  check  and  guarantee 
of  bond,  whether  bids  may  be  submitted  on  portions  of  the  work 
only,  and  any  other  instructions  that  the  work  in  question  may 
seem  to  make  desirable. 

A  clear  and  concise  set  of  instructions  under  the  "  Notice  to 
Bidders  "  will  frequently  simplify  the  comparison  of  the  bids 
after  they  have  been  opened  and  will  avoid  misunderstandings. 

THE  PROPOSAL 

This  is  the  contractor's  bid,  and  should  state  what  he  pro- 
poses to  do.  The  following  form  is  used  by  the  Reclamation 
Service: 

" ,19... 

"  To 

"  SIR: 

"  Pursuant  to  the  foregoing  advertisement,  the  undersigned 
bidder  proposes  to  do  all  the  work  and  to  furnish  all  the  material 
as  provided  by  the  attached  specifications,  and  binds  himself 
on  the  acceptance  of  this  proposal  to  execute  a  contract  with  nec- 
essary bond,  of  which  this  proposal  and  the  said  advertisement 
and  specifications  shall  be  a  part,  for  performing  and  completing 
said  work  within  the  time  required  by  the  specifications  and 
at  the  prices  named  in  the  specifications  and  in  the  schedules 
hereto  annexed. 

"  The  bidder  furthermore  agrees  that,  in  case  of  his  default 
in  executing  a  contract  with  necessary  bond,  the  proceeds  of 
the  check  accompanying  this  proposal  shall  be  and  remain  the 
property  of  the  United  States. 

"  Signature 


"  (Corporate  Seal)  Address  .  . 


318  WORKING   DATA   FOR   IRRIGATION   ENGINEERS 


"  Names  of  individual  members 
of  firm  or  names  and  titles 
of  all  officers  of  corporation 


"  Corporation  organized  under  the  laws  of  the  State  of , 


GUARANTEE  OF  BOND 

This  is  a  simple  statement  signed  by  a  surety  company  or 
by  individual  bondsmen  guaranteeing  that  bond  to  insure  the 
faithful  performance  of  the  work  will  be  furnished  for  the 
bidder  if  contract  is  awarded  to  him.  The  statement  may  be 
as  follows: 

"  We  agree  to  furnish  bond  for  this  bidder,  as  required  by 
these  specifications,  in  case  contract  is  awarded  to  him  on  the 
basis  of  this  proposal. 


Signatures    and    addresses     of 
guarantors  of  bond 


WORK  TO  BE  PERFORMED 

Under  this  head  should  be  stated  the  work  that  is  to  be 
done,  and  appropriate  blanks  should  be  provided  in  which  the 
bidder  can  fill  in  his  prices.  The  work  may  be  listed  by  items 
with  provision  for  a  lump  sum  bid  for  each  item,  or  it  may  be 
in  the  form  of  schedules  of  quantities  in  which  the  quantities  of 
each  class  of  work  are  given  and  blanks  provided  for  the  bidder 
to  fill  in  his  unit  prices  and  total  amounts.  Some  kinds  of  work, 
such  as  machinery,  buildings,  bridges,  etc.,  are  usually  bid  on  by 
the  lump  sum  for  the  entire  job.  Earth- work,  concrete  struc- 
tures, etc.,  are  not  readily  adapted  to  lump-sum  bidding  on 
account  of  uncertainties  existing  in  the  quantities  and  clas- 
sifications. In  such  cases,  it  is  more  satisfactory  to  both  con- 


SPECIFICATIONS  319 

tractor  and  engineer  to  have  an  estimate  of  quantities  and  unit 
prices  for  each  item. 

The  work  to  be  performed  on  large  jobs  may  be  divided  into 
a  number  of  schedules  allowing  the  work  to  be  divided  among  a 
number  of  contractors  if  such  procedure  should  seem  to  be  eco- 
nomical or  desirable.  On  large  jobs  this  allows  small,  as  well  as 
large,  contractors  to  bid  and,  therefore,  results  hi  keener  com- 
petition. 

GENERAL  CONDITIONS 

The  following  general  clauses  are  used  by  the  Reclamation 
Service  in  all  specifications.  (Paragraphs  20  to  28  inclusive  are 
not  used  when  they  are  not  required,  such  as  in  specifications 
for  furnishing  machinery,  cement,  and  other  materials.)  Special 
clauses  applying  exclusively  to  Government  work  and  reference 
to  Government  bureaus  and  officers  have  been  omitted.  Some 
clauses  and  words  unnecessary  for  private  contracts  have  been 
modified  or  eliminated.  Particular  attention  is  called  to  the 
fact  that  these  general  clauses  must  be  used  with  discretion,  as 
they  cover  most  of  the  legal  requirements  by  which  the  con- 
tractor is  to  be  bound,  and  it  is  desirable,  especially  on  im- 
portant works,  to  have  them  reviewed  by  a  legal  expert. 

i.  Form  of  Proposal  and  Signature. — The  proposal  shall  be 
made  on  the  form  provided  therefor  and  shall  be  enclosed  in  a 
sealed  envelope  marked  and  addressed  as  required  in  the  notice 
to  bidders.  The  bidder  shall  state  in  words  and  in  figures  the 
unit  prices  or  the  specific  sums,  as  the  case  may  be,  for  which 
he  proposes  to  supply  the  material  or  machinery  and  perform 
the  work  required  by  these  specifications.  If  the  proposal  is 
made  by  an  individual  it  shall  be  signed  with  his  full  name,  and 
his  address  shall  be  given;  if  it  is  made  by  a  firm,  it  shall  be 
signed  with  the  copartnership  name  by  a  member  of  the  firm, 
and  the  name  and  full  address  of  each  member  shall  be  given; 
and  if  it  is  made  by  a  corporation  it  shall  be  signed  by  an  officer 
with  the  corporate  name  attested  by  the  corporate  seal,  and  the 
names  and  titles  of  all  officers  of  the  corporation  shall  be  given. 
No  telegraphic  proposal  or  telegraphic  modification  of  a  proposal 
will  be  considered. 


320  WORKING  DATA  FOR  IRRIGATION   ENGINEERS 

2.  Proposal. — Blank  spaces  in  the  proposal  should  be  prop- 
erly filled.     The  phraseology  of  the  proposal  should  not  be 
changed,  and  no  additions  should  be  made  to  the  items  men- 
tioned therein.    Unauthorized  conditions,  limitations,  or  provisos 
attached  to  a  proposal  will  render  it  informal  and  may  cause  its 
rejection.     Alterations   by   erasure   or   interlineation  must  be 
explained  or  noted  in  the  proposal  over  the  signature  of  the 
bidder.     If  the  unit  price  and  the  total  amount  named  by  a 
bidder  for  any  item  do  not  agree,  the  unit  price  alone  will  be 
considered  as  representing  the  bidder's  intention.     A  bidder 
may  withdraw  his  proposal  before  the  expiration  of  the  time 
during  which  proposals  may  be  submitted,  without  prejudice  to 
himself,  by  submitting  a  written  request  for  its  withdrawal  to 
the  officer  who  holds  it.    No  proposals  received  after  said  time 
will  be  considered.     Bidders  are  invited  to  be  present  at  the 
opening  of  proposals.     The  right  is  reserved  to  reject  any  or 
all  proposals,  to  accept  one  part  of  a  proposal  and  reject  the  other, 

and  to  waive  technical  defects,  as  the  interests  of 

may  require. 

3.  Certified  Check. — Each  bidder  shall  submit  with  his  pro- 
posal a  certified  check  for  the  sum  stated  in  the  notice  to  bidders, 

drawn  to  the  order  of If  the  bidder  to  whom 

an  award  is  made  fails  or  refuses  to  execute  the  required  contract 
and  bond  within  the  time  specified  in  paragraph  4,  the  proceeds 

of  his  check  shall  become  the  property  of The 

proceeds  of  the  check  of  the  successful  bidder  will  be  returned 
after  the  execution  of  his  contract  and  the  approval  of  his  bond 

on  behalf  of ;  and  the  proceeds  of  the  checks  of 

the  other  bidders  will  be  returned  at  the  expiration  of  ....  days 
from  the  date  of  opening  proposals,  or  sooner  if  contract  is  exe- 
cuted prior  to  that  time. 

4.  The  Contract. — The  bidder  to  whom  an  award  is  made 

shall  execute  a  written  contract  with and  if  bond 

is  required  furnish  good  and  approved  bond  within  ....  days 
after  receiving  the  forms  of  contract  and  bond  for  execution. 
If  the  bidder  to  whom  an  award  is  made  fails  to  enter  into  a 
contract  as  herein  provided,  the  award  will  be  annulled,  and  an 
award  may  be  made  to  the  bidder  whose  proposal  is  next  most 


SPECIFICATIONS  321 

acceptable  in  the  opinion  of ;  and  such  bidder 

shall  fulfill  every  stipulation  embraced  herein  as  if  he  were  the 
party  to  whom  the  first  award  was  made.  The  advertisement, 
notice  to  bidders,  proposal,  general  conditions,  and  detail  specifi- 
cations and  drawings  will  be  incorporated  in  the  contract.  A 
corporation  to  which  an  award  is  made  may  be  required,  before 
the  contract  is  finally  executed,  to  furnish  certificate  of  its  cor- 
porate existence  and  evidence  that  the  officer  signing  the  con- 
tract for  the  corporation  is  duly  authorized  to  do  so. 

5.  Contractor's  Bond. — The  contractor  shall  furnish  bond  in 

an  amount  not  less  than per  cent  of  the  estimated  aggregate 

payments  to  be  made  under  the  contract,  conditioned  upon  the 
faithful  performance  by  the  contractor  of  all  covenants  and  stip- 
ulations in  the  contract.    If  during  the  continuance  of  the  con- 
tract any  of  the  sureties  die,  or,  in  the  opinion  of , 

are  or  become  irresponsible,  the may  require 

additional  sufficient  sureties,  which  the  contractor  shall  furnish 
to  the  satisfaction  of  that  officer  within  ....  days  after  notice. 

6.  Engineer. — The  word  "  engineer  "  used  in  these  specifi- 
cations or  in  the  contract  means He  will  be 

represented  by  assistants  and  inspectors  authorized  to  act  for 
him.    On  all  questions  concerning  the  acceptability  of  material 
or  machinery,  the  classification  of  material,  the  execution  of  the 
work,   conflicting  interests  of  contractors  performing  related 
work,  and  the  determination  of  costs,  the  decision  of  the  engineer 
shall  be  final. 

7.  Contractor. — The    word    "  contractor "    used    in    these 
specifications  or  in  the  contract  means  the  person,  firm,  or  cor- 
poration with  whom  the  contract  is  made  by 

The  contractor  shall  at  all  times  be  represented  on  the  works  in 
person  or  by  a  foreman  or  duly  designated  agent.    Instructions 
and  information  given  by  the  engineer  to  the  contractor's  fore- 
man or  agent  on  the  work  shall  be  considered  as  having  been 
given  to  the  contractor.    When  two  or  more  contractors  are  en- 
gaged on  installation  or  construction  work  in  the  same  vicinity 
the  engineer  shall  be  authorized  to  direct  the  manner  in  which 
each   shall   conduct    his    work    so    far    as    it    affects    other 
contractors. 


322  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

8.  Materials  and  Workmanship.— All  materials  must  be  of 
the  specified  quality  and  equal  to  approved  samples,  if  samples 
have  been  submitted.    All  work  shall  be  done  and  completed  in 
a  thorough,  workmanlike  manner,  notwithstanding  any  omission 
from  these  specifications  or  the  drawings.    All  materials  furnished 
and  all  work  done  must  be  satisfactory  to  the  engineer.    Work  not 
in  accordance  with  these  specifications,  in  the  opinion  of  the 
engineer,  shall  be  made  to  conform  thereto.     Unsatisfactory 
material  will  be  rejected,  and,  if  so  ordered  by  the  engineer, 
shall,  at  the  contractor's  expense,  be  immediately  removed  from 
the  vicinity  of  the  work. 

9.  Delays. — The  contractor  shall  receive  no  compensation 
for  delays  or  hindrances  to  the  work  except  when,  in  the  judg- 
ment of  the  engineer,  direct  and  unavoidable  extra  cost  to  the 
contractor  is  caused  by  the  failure  of  the to  pro- 
vide necessary  information,  material,  right  of  way,  or  site  for 
installation.    When  such  extra  compensation  is  claimed  a  written 
statement  thereof  shall  be  presented  by  the  contractor  not  later 
than  ....  days  after  the  close  of  the  month  during  which  extra 
cost  is  claimed  to  have  been  incurred.     Such  claim,  if  found 
correct,  will  be  approved  and  the  decision  of  the  engineer,  whether 
extra  cost  has  been  incurred  and  the  amount  thereof,  shall  be 
final.    If  delays  are  caused  by  specific  orders  to  stop  work  given 
by  the  engineer,  or  by  the  performance  of  extra  work,  or  by  un- 
foreseen causes  beyond  the  control  of  the  contractor,  or  by  the 
failure  of  to  provide  material  or  necessary  in- 
structions for  carrying  on  the  work  or  to  provide  the  necessary 
right  of  way  or  site  for  installation,  then  such  delay  will  entitle 
the  contractor  to  an  equivalent  extension  of  time. 

10.  Changes. — The  engineer  may,  without  notice  to  the  sure- 
ties on  the  contractor's  bond,  make  such  changes  in  the  designs 
of  materials  or  machinery  or  plans  for  installation  or  construction 
or  in  the  quantities  or  character  of  the  work  or  material  required 
as  he  may  deem  advisable.    These  changes  in  plans  for  installa- 
tion or  construction  may  also  include  modifications  of  shapes 
and  dimensions  of  canals,  dams,  and  other  structures,  and  the 
shifting  of  locations  to  suit  conditions  disclosed  as  work  pro- 
gresses.   If  such  changes  result  in  an  increase  or  decrease  of  cost 


SPECIFICATIONS  323 

to  the  contractor,  the  engineer  will  make  such  additions  or  de- 
ductions on  account  thereof  as  he  may  deem  reasonable  and 
proper  and  his  action  thereon  shall  be  final.  Extra  work  or 
material  shall  be  charged  for  as  hereinafter  provided. 

11.  Extra  Work  or  Material. — In  connection  with  the  work 
covered  by  this  contract,  the  engineer  may  order  work  or  material 
not  covered  by  the  specifications.    Such  work  or  material  will  be 
classed  as  extra  work  and  will  be  ordered  in  writing.     No  extra 
work  will  be  paid  for  unless  ordered  in  writing.     Extra  work 
shall  be  charged  for  at  actual  necessary  cost,  as  determined  by 
the  engineer,  plus  ....  per  cent  for  profit,  superintendence,  and 
general  expenses.     The  actual  necessary  cost  will  include  all 
expenditures  for  materials,  labor,  and  supplies  furnished  by  the 
contractor,   and  a  reasonable  allowance  for  the  use  of  shop 
equipment  where  required,  but  will  not  include  any  allowance 
for  office  expenses,  general  superintendence,  or  other  general 
expenses.    At  the  end  of  each  month  the  contractor  shall  present 
in  writing  his  claims  for  extra  work  and  material  and,  when 
requested  by  the  engineer,  shall  furnish  itemized  statements  of 
the  cost  and  shall  permit  examination  of  accounts,  bills,  and 
vouchers  relating  thereto. 

12.  Inspection. — All   materials    furnished    and   work    done 
under  this  contract  will  be  subject  to  rigid  inspection.     The 
contractor  shall  furnish  complete  facilities,  including  the  neces- 
sary labor  for  the  inspection  of  all  material  and  workmanship. 
The  engineer  shall  have  at  all  times  access  to  all  parts  of  the 
shop  where  such  material  under  his  inspection  is  being  manufac- 
tured.    Material  that  does  not  conform  to  the  specifications, 
accepted  through  oversight  or  otherwise,  may  be  rejected  at  any 
stage  of  the  work.    Whenever  the  contractor  on  installation  or 
construction  is  permitted  or  directed  to  do  night  work  or  to  vary 
the  period  during  which  work  is  carried  on  each  day,  he  shall 
give  the  engineer  due  notice,  so  that  inspection  may  be  pro- 
vided for. 

13.  Errors  and  Omissions. — The  contractor  will  not  be  al- 
lowed to  take  advantage  of  any  error  or  omission  in  these  speci- 
fications.   Suitable  instructions  will  be  given  when  such  error  or 
omission  is  discovered. 


324  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

14.  Experience. — Bidders,  if  required,  shall  present  satisfac- 
tory evidence  that  they  have  been  regularly  engaged  in  furnishing 
material  and  machinery  and  constructing  such  work  as  they  pro- 
pose to  execute,  and  that  they  are  fully  prepared  with  necessary 
capital,  machinery,  and  material  to  begin  the  work  promptly 
and  to  conduct  it  as  required  by  these  specifications. 

15.  Specifications  and  Drawings. — The  contractor  shall  keep 
on  the  work  a  copy  of  the  specifications  and  drawings  and  shall 
at  all  times  give  the  engineer  access  thereto.    Any  drawings  or 
plans  listed  in  the  detail  specifications  shall  be  regarded  as  part 
thereof  and  of  the  contract.    Anything  mentioned  in  these  speci- 
fications and  not  shown  in  the  drawings  or  shown  in  the  drawings 
and  not  mentioned  in  these  specifications  shall  be  done  as 
though  shown  or  mentioned  in  both.    The  engineer  will  furnish 
from  time  to  time  such  detail  drawings,  plans,  profiles,  and 
information  as  he  may  consider  necessary  for  the  contractor's 
guidance. 

16.  Local  Conditions. — Bidders  shall  satisfy  themselves  as  to 
local  conditions  affecting  the  work,  and  no  information  derived 
from  the  maps,  plans,  specifications,  profiles,  or  drawings,  or 
from  the  engineer  or  his  assistants,  will  relieve  the  contractor 
from  any  risk  or  from  fulfilling  all  of  the  terms  of  his  contract. 
The  accuracy  of  the  interpretation  of  the  facts  disclosed  by  bor- 
ings  or   other   preliminary   investigations   is   not   guaranteed. 
Each  bidder  or  his  representative  should  visit  the  site  of  the 
work  and  familiarize  himself  with  local  conditions;  failure  to  do 
so  when  intelligent  preparation  of  bid  depends  on  a  knowledge 
of  local  conditions  may  be  considered  sufficient  cause  for  rejecting 
a  proposal. 

17.  Data  to  be  Furnished  by  the  Contractor. — The  contractor 
shall  furnish  the  engineer  reasonable  facilities  for  obtaining  such 
information  as  he  may  desire  respecting  the  character  of  the 
materials  and  the  progress  and  manner  of  the  work,  including  all 
information  necessary  to  determine  its  cost,  such  as  the  number 
of  men  employed,  their  pay,  the  time  during  which  they  worked 
on  the  various  classes  of  construction,  etc. 

1 8.  Damages. — The  contractor  will  be  held  responsible  for 
and  required  to  make  good,  at  his  own  expense,  all  damage  to 


SPECIFICATIONS  325 

person  or  property  caused  by  carelessness  or  neglect  on  the  part 
of  the  contractor,  his  agent  or  employees. 

19.  Character  of  Workmen. — The  contractor  shall  not  allow 
his  agents  or  employees  to  trespass  on  premises  or  lands  in  the 
vicinity  of  the  work.    None  but  skilled  foremen  and  workmen 
shall  be  employed  on  work  requiring  special  qualifications,  and 
when  required  by  the  engineer,  the  contractor  shall  discharge 
any  person  who  commits  trespass  or  is  in  the  opinion  of  the 
engineer  disorderly,  dangerous,  insubordinate,  incompetent,  or 
otherwise  objectionable. 

20.  Staking  Out  Work. — The  work  to  be  done  will  be  staked 
out  for  the  contractor,  who  shall  provide  such  material  and  give 
such  assistance  as  may  be  required  by  the  engineer. 

21.  Methods  and  Appliances. — The  methods  and  appliances 
adopted  by  the  contractor  shall  be  such  as  will,  in  the  opinion  of 
the  engineer,  secure  a  satisfactory  quality  of  work  and  will 
enable  the  contractor  to  complete  the  work  in  the  time  agreed 
upon.    If  at  any  time  the  methods  and  appliances  appear  inad- 
equate, the  engineer  may  order  the  contractor  to  improve  their 
character  or  efficiency,  and  the  contractor  shall  conform  to  such 
order;  but  failure  of  the  engineer  to  order  such  improvement  of 
methods  or  efficiency  will  not  relieve  the  contractor  from  his 
obligation  to  perform  satisfactory  work  and  to  finish  it  in  the 
time  agreed  upon. 

22.  Climatic  Conditions. — The  engineer  may  order  the  con- 
tractor to  suspend  any  work  that  may  be  damaged  by  climatic 
conditions.    When  delay  is  caused  by  an  order  to  suspend  work 
given  on  account  of  climatic  conditions  that  could  have  been 
reasonably  foreseen  the  contractor  will  not  be  entitled  to  any 
extension  of  time  on  account  of  such  order. 

23.  Quantities  and  Unit  Prices. — The  quantities  noted  in 
the  schedule  or  proposal  are  approximations  for  comparing  bids, 
and  no  claim  shall  be  made  against  the  United  States  for  excess 
or  deficiency  therein,  absolute  or  relative.     Payment  at  the 
prices  agreed  upon  will  be  in  full  for  the  completed  work  and 
will  cover  materials,  supplies,  labor,  tools,  machinery,  and  all 
other  expenditures  incident  to  satisfactory  compliance  with  the 
contract. 


326  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

24.  Removal  and  Rebuilding  of  Defective  Work. — The  con- 
tractor shall  remove  and  rebuild  at  his  own  expense  any  part  of 
the  work  that  has  been  improperly  executed,  even  though  it 
has  been  included  in  the  monthly  estimates.     If  he  refuses  or 
neglects  to  replace  such  defective  work,  it  may  be  replaced  by 
at  the  contractor's  expense. 

25.  Protection  of  Work  and  Cleaning  Up. — The  contractor 
shall  be  responsible  for  any  material  furnished  him  and  for  the 
care  of  all  work  until  its  completion  and  final  acceptance,  and  he 
shall  at  his  own  expense  replace  damaged  or  lost  material  and 
repair  damaged  parts  of  the  work,  or  the  same  may  be  done  at 

his  expense  by  He  shall  take  all  risks  from 

floods  and  casualties  and  shall  make  no  charge  for  detention 
from  such  causes.    He  may,  however,  be  allowed  a  reasonable 
extension  of  time  on  account  of  such  detention,  subject  to  the 
conditions  hereinbefore  specified.    The  contractor  shall  remove 
from  the  vicinity  of  the  completed  work  all  plant,  buildings, 
rubbish,  unused  material,  concrete  forms,  etc.,  belonging  to  him 
or  used  under  his  direction  during  construction,  and  in  the 
event  of  his  failure  to  do  so  the  same  may  be  removed  by 
at  his  expense. 

26.  Roads  and  Fences. — Roads  subject  to  interference  from 
the  work  covered  by  this  contract  shall  be  kept  open,  and  the 
fences  subject  to  interference  shall  be  kept  up  by  the  contractor 
until  the  work  is  finished. 

27.  Bench  Marks  and  Survey  Stakes. — Bench  marks  and 
survey  stakes  shall  be  preserved  by  the  contractor  and  in  case 
of  their  destruction  or  removal  by  him  or  his  employees,  they 
will  be  replaced  by  the  engineer  at  the  contractor's  expense. 

28.  Sanitation.  — The  engineer  may  establish  sanitary  and 
police  rules  and  regulations  for  all  forces  employed  under  this 
contract;  and  if  the  contractor  fails  to  enforce  these  rules  the 
engineer  may  enforce  them  at  the  expense  of  the  contractor. 

DETAIL    SPECIFICATIONS 

The  detail  specifications  should  state  in  specific  terms,  as  far 
as  possible,  the  exact  nature  and  quality  of  work  that  the  con- 
tractor will  be  required  to  perform  so  that  he  will  be  enabled  to 


SPECIFICATIONS  327 

formulate  an  intelligent  bid.  No  important  requirements  as  far 
as  they  are  known  should  be  omitted;  neither  should  re- 
quirements be  inserted  which  it  is  not  intended  to  enforce.  The 
latter  practice  has  resulted  in  the  tendency  of  contractors  to 
assume  that  certain  requirements  will  not  be  enforced  with 
resultant  detriment  to  all  concerned.  The  more  thorough  the 
understanding  between  the  contractor  and  engineer  before  the 
bid  is  submitted,  the  more  satisfactory  will  be  the  results. 

It  is  not  intended  by  the  above  remarks  to  imply  that  require- 
ments established  before  a  contract  is  let  must  be  adhered  to 
under  all  circumstances.  It  is  probably  safe  to  say  that  there 
have  been  few  large  works  constructed  the  specifications  for 
which  did  not  have  to  be  modified  in  certain  details.  There 
should,  however,  be  special  reasons  for  such  modifications,  and 
when  modifications  are  made  without  such  reasons  there  is  evi- 
dence of  laxity  on  the  part  of  the  engineer  in  enforcing  the  re- 
quirements, or  his  specifications  must  have  been  poorly  drawn. 
Happily  for  the  engineering  profession,  the  former  happens  very 
infrequently.  The  latter  is  usually  due  to  lack  of  knowledge  of 
the  work  to  be  done  or  of  current  practice  in  regard  thereto. 

It  can  hardly  be  expected  of  an  engineer  to  have  a  personal 
and  detailed  knowledge  of  the  requirements  of  all  the  work 
coming  under  his  supervision,  and  this  lack  of  knowledge  may 
sometimes  show  up  in  his  specifications.  It  is  customary,  where 
the  requirements  in  regard  to  details  are  not  definitely  known,  to 
leave  the  specifications  open  on  such  points  and  to  require  that 
the  contractor  submit  his  own  specifications,  which  shall  be  sub- 
ject to  the  approval  of  the  engineer.  This  also  applies  to  detail 
designs.  This  procedure  is  also  followed  when  it  is  intended 
that  contractors  shall  submit  bids  on  their  standard  goods. 

The  above  remarks  in  regard  to  the  detail  specifications 
apply  also  to  the  drawings.  Complete  detail  drawings  are 
not  always  necessary,  nor  even  desirable,  as  the  details  are 
nearly  always  changed  after  the  work  has  gotten  under  way,  and 
such  detail  drawings  can  be  supplied  after  the  contract  has  been 
let.  The  main  thing  to  be  kept  in  mind  is  that  all  items  and 
conditions  affecting  the  cost  to  the  contractor  of  doing  the  work 
should  be  shown  on  the  drawings  as  far  as  this  is  possible. 


328  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

SPECIAL   CONDITIONS 
i.  Description  of  Work. — 


2.   List  of  Drawings. — 


3.  Commencement,  Prosecution,  and  Completion  of  Work.— 

Work  shall  be  commenced  by  the  contractor  within  ....  days, 
and  shall  be  completed  within  ....  days  after  the  execution  of 

the  contract  on  behalf  of The  contractor  shall 

at  all  times  during  the  continuation  of  the  contract  prosecute 
the  work  with  such  force  and  equipment  as,  in  the  judgment  of 
the  engineer,  are  sufficient  to  complete  it  within  the  specified  time. 

4.  Failure  to  Complete  the  Work  in  the  Time  Agreed  Upon.— 
Should  the  contractor  fail  to  complete  the  work  or  any  part 
thereof  in  the  time  agreed  upon  in  the  contract,  or  in  such  extra 

time  as  may  have  been  allowed  for  delays,  a  deduction  of 

dollars  per  day  for  each  schedule  will  be  made  for  each  and  every 
day,  including  Sundays  and  holidays,  that  such  schedule  remains 
uncompleted  after  the  date  required  for  the  completion.    The 
said  amounts  are  hereby  agreed  upon  as  liquidated  damages  for 

the  loss  to  on  account  of  all  expenses  due  to 

the  employment  of  engineers,  inspectors,  and  other  employees 
after  the  expiration  of  the  time  for  completion  and  on  account 
of  the  value  of  the  operation  of  the  irrigation  works  dependent 
thereon,  and  will  be  deducted  from  any  money  due  the  con- 
tractor under  this  contract,  and  the  contractor  and  his  sureties 
shall  be  liable  for  any  excess. 

5.  Progress  Estimates  and  Payments. — At  the  end  of  each 
calendar  month  the  engineer  will  make  an  approximate  measure- 
ment of  all  work  done  and  material  delivered  up  to  that  date, 
classified  according  to  items  named  in  the  contract,  and  will  make 
an  estimate  of  the  value  of  the  same  on  the  basis  of  the  unit 
prices  named  in  the  contract.    To  the  estimate  made  as  above 
set  forth  will  be  added  the  amounts  earned  for  extra  work  to  the 
date  of  the  progress  estimate.    From  the  total  thus  computed  a 
deduction  of  10  per  cent  will  be  made  and  from  the  remainder 

there  will  be  further  deducted  any  amount  due  to 

from  the  contractor  for  supplies  or  materials  furnished  or  services 


SPECIFICATIONS  329 

rendered  and  any  other  amounts  that  may  be  due  to 

as  damages  for  delays  or  otherwise  under  the  terms  of  the  con- 
tract. From  the  balance  thus  determined  will  be  deducted  the 
amount  of  all  previous  payments  and  the  remainder  will  be  paid 
to  the  contractor  upon  the  approval  of  the  accounts.  The  10  per 
cent  deducted  as  above  set  forth  will  become  due  and  payable 
with  and  as  a  part  of  the  final  payment  to  be  made  as  hereinafter 
provided.  When  the  terms  of  the  contract  shall  have  been  fully 
complied  with  to  the  satisfaction  of  the  engineer  and  when  a 

release  of  all  claims  against under  or  by  virtue 

of  the  contract  shall  have  been  executed  by  the  contractor,  final 
payment  will  be  made  of  any  balance  due,  including  the  per- 
centage withheld  as  above,  or  such  portion  thereof  as  may  be 
due  to  the  contractor. 

Note. — Under  the  head  of  "  Special  Conditions  "  should  also 
be  stated  any  other  requirements  or  conditions  applying  to  the 
particular  contract  as  a  whole. 

SPECIFICATIONS  FOR  CANAL  EXCAVATION 

i.  Classification  of  Excavation. — All  materials  moved  in  the 
excavation  of  canals  and  for  structures,  and  in  the  construction 
of  embankments  will  be  measured  in  excavation  only,  to  the 
neat  lines  shown  in  the  drawings  or  prescribed  by  the  engineer, 
and  will  be  classified  for  payment  as  follows: 

Class  1. — Material  that  can  be  ploughed  to  a  depth  of  six 
inches  or  more  with  a  six-horse  or  six-mule  team,  each  animal 
weighing  not  less  than  1,400  pounds,  attached  to  a  suitable 
plough,  all  well  handled  by  at  least  three  men;  also  all  material 
that  is  loose  and  can  be  handled  in  scrapers,  and  all  detached 
masses  of  rock,  not  exceeding  two  cubic  feet  in  volume,  occurring 
in  loose  material  or  material  that  can  be  ploughed  as 
specified. 

Class  2. — Indurated  material  of  all  kinds  that  cannot  be 
ploughed  as  described  under  Class  1,  but  that,  when  loosened  by 
powder  or  other  suitable  means,  can  be  removed  by  the  use  of 
ploughs  and  scrapers,  and  all  detached  masses  of  rock  more  than 
two  and  not  exceeding  ten  cubic  feet  in  volume. 

Class  3. — All  rock  in  place  not  included  in  Classes  1  and  2, 


330  WORKING  DATA  FOR   IRRIGATION  ENGINEERS 

and  all  detached  masses  of  rock  exceeding  ten  cubic  feet  in  vol- 
ume, not  included  in  Classes  1  and  2. 

Note:  The  above  classifications  may  also  be  used  for  "wet" 
excavation,  but  provision  must  be  made  for  separate  prices  for 
wet  excavation. 

If  there  be  required  the  excavation  of  any  material  which,  in 
the  opinion  of  the  engineer,  cannot  properly  be  included  in  any 
of  the  above  three  classes,  the  engineer  will  determine  the  actual 
necessary  cost  of  excavating  and  disposing  of  such  material,  and 
payment  therefor  as  extra  work  will  be  made  under  the  provi- 
sions of  paragraph  ....  of  these  specifications.  No  additional 
allowance  above  the  prices  bid  for  the  several  classes  of  material 
will  be  made  on  account  of  any  of  the  material  being  frozen.  It 
is  desired  that  the  contractor  or  his  representative  be  present 
during  the  measurement  of  material  excavated.  On  written 
request  of  the  contractor,  made  by  him  within  ten  days  after 
the  receipt  of  any  monthly  estimate,  a  statement  of  the  quan- 
tities and  classifications  between  successive  stations  included  in 
said  estimate  will  be  furnished  him  within  ten  days  after  the 
receipt  of  such  request.  This  statement  will  be  considered  as 
satisfactory  to  the  contractor  unless  he  files  with  the  engineer, 
in  writing,  specific  objections  thereto,  with  reasons  therefor, 
within  ten  days  after  receipt  of  said  statement  by  the  contractor 
or  his  representative  on  the  work.  Failure  to  file  such  written 
objection  with  reason  therefor  within  said  ten  days  shall  be 
considered  a  waiver  of  all  claims  based  on  alleged  erroneous 
estimate  of  quantities  or  incorrect  classification  of  materials  for 
the  work  covered  by  such  statement. 

2.  Canal  Sections. — The  canal  sections  are  shown  in  the 
drawings,  but  the  undetermined  stability  of  the  material  that 
will  form  the  canal  banks  may  make  it  desirable  during  the 
progress  of  the  work  to  vary  the  slopes  and  dimensions  depen- 
dent thereon.  Increase  or  decrease  of  quantities  excavated  as  a 
result  of  such  changes  shall  be  covered  in  the  estimates  and  shall 
not  otherwise  affect  the  payments  due  to  contractor,  unless  it 
is  found  by  the  engineer  that  the  unit  cost  is  thereby  increased, 
in  which  case  the  engineer  will  estimate,  and  include  in  the 
amount  due  the  contractor,  the  amount  of  such  increase.  The 


SPECIFICATIONS  331 

canal  shall  be  excavated  to  the  full  depth  and  width  required 
and  must  be  finished  to  the  prescribed  lines  and  grades  in  a  work- 
manlike manner.  Runways  shall  not  be  cut  into  canal  slopes 
below  the  proposed  water  level.  Earth  slopes  shall  be  neatly 
finished  with  scrapers  or  similar  appliances.  Rock  bottoms  and 
banks  must  show  no  points  of  rock  projecting  more  than  0.3  foot 
into  the  prescribed  section.  Above  the  water  line  the  rock  will 
be  allowed  to  stand  at  its  steepest  safe  angle  and  no  finishing 
will  be  required  other  than  the  removal  of  rock  masses  that  are 
loose  and  liable  to  fall.  Payment  for  excavation  of  canals  will 
be  made  to  the  neat  lines  only  as  shown  in  the  drawings  or  as 
established  by  the  engineer. 

3.  Preparation  of  Surfaces. — The  ground  under  all  embank- 
ments that  are  to  sustain  water  pressure,  and  the  surface  of  all 
excavation  that  is  to  be  used  for  embankments,  shall  be  cleared 
of  trees,  brush,  and  vegetable  matter  of  every  kind.    The  roots 
shall  be  grubbed  and  burned  with  other  combustible  material 
that  has  been  removed.    The  surface  of  the  ground  under  the 
entire  embankment  shall  be  scored  with  a  plough  making  open 
furrows  not  less  than  eight  inches  deep  below  the  natural  ground 
surface  at  intervals  of  not  more  than  three  feet.    The  cost  of  all 
work  described  in  this  paragraph  shall  be  included  in  the  unit 
prices  bid  for  excavation. 

4.  Construction  of  Embankments. — Embankments  built  with 
teams  and  scrapers  or  with  dump  wagons  shall  be  made  in  layers 
not  exceeding  twelve  inches  in  thickness  and  kept  as  level  as 
practicable.    The  travel  over  the  embankments  during  construc- 
tion shall  be  so  directed  as  to  distribute  the  compacting  effect  to 
the  best  advantage.    Any  additional  compacting  required  over 
that  produced  by  ordinary  travel  in  distributing  the  material  will 
be  ordered  in  writing  and  paid  for  as  extra  work  under  the  pro- 
visions of  paragraph Embankments  shall  be  built  to  the 

height  designated  by  the  engineer  to  allow  for  settlement,  and 
shall  be  levelled  on  top  to  a  regular  grade.  ( Note. — //  the  engineer 
proposes  to  permit  the  use  of  machinery  in  canal  excavation  full 
specifications  should  be  drafted  in  each  individual  case.    Machine- 
built  embankments  must  generally  be  rolled  to  make  them  equal 
in  value  to  team-built  embankments    and,  in    order    to  be  eco- 


I 

332  WORKING  DATA  FOR   IRRIGATION  ENGINEERS 

nomical,  machine-work  should  be  several  cents  cheaper  per  cubic 
yard  than  team-work.)  No  embankments  shall  be  made  from 
frozen  materials  nor  on  frozen  surfaces.  Should  the  engineer 
direct  that  unsuitable  material  be  excavated  and  removed 
from  the  site  of  any  embankment,  the  material  thus  exca- 
vated will  be  paid  for  as  excavation.  When  canal  excava- 
tion precedes  the  building  of  structures,  openings  shall  be 
left  in  the  embankments  at  the  sites  of  these  structures, 
and,  except  when  the  construction  of  the  structures  is  included 
in  the  contract,  the  contractor  will  not  be  required  to  complete 
such  omitted  embankments.  The  cost  of  all  work  described  in 
this  paragraph,  except  as  herein  specified,  shall  be  included  in 
the  prices  bid  for  excavation. 

5.  Disposal  of  Materials. — All  suitable  material  excavated  in 
the  construction  of  canals  and  structures,  or  so  much  thereof 
as  may  be  needed,  shall  be  used  in  the  construction  of  embank- 
ments and  in  backfilling  around  structures.  Where  the  canal  is 
on  sloping  ground,  all  material  taken  from  the  excavation  shall 
be  deposited  on  the  lower  side  of  the  canal  unless  otherwise  shown 
in  the  drawings  or  directed  by  the  engineer.  Where  the  canal  is 
on  level  or  nearly  level  ground,  the  material  from  the  excavation 
shall  be  deposited  in  embankments  on  both  sides  to  form  the  top 
portions  of  the  waterway.  If  there  is  an  excess  of  material  in 
excavation,  it  shall  be  used  to  strengthen  the  embankment  on 
either  side  of  the  canal  as  may  be  directed  by  the  engineer. 
Material  taken  from  cuts  that  is  not  suitable  for  embankment 
construction  and  surplus  material  may  be  wasted  on  the  right  of 
way  owned  by  ,  at  such  points  as  shall  be  ap- 
proved by  the  engineer.  Unless  otherwise  shown  in  the  drawings 
or  directed  by  the  engineer,  no  material  shall  be  wasted  in  drain- 
age channels,  nor  within  ....  feet  of  the  edge  of  the  prescribed 
or  actual  canal  cut.  On  side-hill  locations  all  material  wasted 
shall  be  placed  on  the  lower  side  of  the  canal  unless  specific 
written  authority  is  obtained  from  the  engineer  to  waste  such 
material  elsewhere.  Waste  banks  shall  be  left  with  reasonably 
even  and  regular  surfaces.  Whenever  directed  by  the  engineer, 
materials  found  in  the  excavation,  such  as  sand,  gravel,  or  stone, 
that  are  suitable  for  use  in  structures  or  that  are  otherwise  re- 


SPECIFICATIONS  333 

quired  for  special  purposes,  shall  be  preserved  and  laid  aside  in 
some  convenient  place  designated  by  him. 

6.  Borrow  Pits. — Where  the  canal  excavation  at  any  section 
does  not  furnish  sufficient  suitable  material  for  embankments, 
the  engineer  will  designate  where  additional  material  shall  be  pro- 
cured.   Unless  otherwise  shown  on  the  drawings  or  directed  by 
the  engineer  a  berm  of  fifteen  feet  shall  be  left  between  the 
outside  toe  of  the  embankment  and  the  edge  of  the  borrow  pit, 
with  provision  for  a  side  slope  of  one  and  one-half  to  one  to  the 
bottom  of  the  borrow  pit.    Borrowed  material  will  be  measured 
in  excavation  only,  and  unless  the  engineer  gives  the  contractor 
specific  written  orders  to  excavate  other  than  class  1  material 
from  borrow  pits,  all  material  obtained  from  this  source  will  be 
paid  for  at  the  unit  price  bid  for  class  1  excavation,  regardless  of 
its  actual  character.    Payment  for  excavation  from  borrow  pits 
will  be  made  for  only  such  quantities  as  are  required  for  embank- 
ments or  backfilling  or  such  as  by  direction  of  the  engineer  are 
excavated  and  wasted  or  laid  aside. 

7.  Overhaul. — All  material  taken  from  the  excavation  and 
required  for  embankment  or  for  other  purposes  shall  be  placed 
as  directed  by  the  engineer.    The  limit  of  free  haul  will  be  200 
feet.    Necessary  haul  over  200  feet  will  be  paid  for  at  the  price 
bid  ( Note. — If  it  is  desirable,  a  fixed  sum  should  be  stated  for  over- 
haul] per  cubic  yard  per  hundred  feet  additional  haul,  but  no 
allowance  will  be  made  for  overhaul  where  the  excavated  material 
is  wasted,  except  where  such  overhaul  is  specifically  ordered  in 
writing  by  the  engineer.    Where  material  is  taken  from  borrow 
pits,  the  length  of  the  haul  will  be  measured  along  the  shortest 
practicable  route  between  the  center  of  gravity  of  the  material  as 
found  in  excavation  and  the  center  of  gravity  of  the  material  as 
deposited  in  each  station.     Where  the  material  is  taken  from 
canal  excavation,  the  length  of  the  haul  shall  be  understood  to 
mean  the  distance  measured  along  the  center  line  of  the  canal 
from  the  center  of  gravity  of  the  material  as  found  in  excavation 
to  the  center  of  gravity  of  the  material  as  required    to  be 
deposited. 

8.  Surface  and  Berm  Ditches. — If,  in  the  judgment  of  the 
engineer,  it  should  be  necessary  to  construct  surface  and  berm 


334  WORKING   DATA   FOR   IRRIGATION   ENGINEERS 

drainage  ditches  along  the  lines  of  the  canal,  the  contractor 
shall  perform  such  work  and  the  excavation  will  be  paid  for  at 
the  unit  prices  bid  in  the  schedules  covering  the  excavation  of 
the  canal  along  which  such  surface  and  berm  ditches  are  built. 
9.  Blasting. — Any  blasting  that  will  probably  injure  the  work 
will  not  be  permitted,  and  any  damage  done  to  the  work  by  blast- 
ing shall  be  repaired  by  the  contractor  at  his  expense. 

SPECIFICATIONS    FOR    TUNNELS 

1.  Excavation. — The  tunnel,  shafts,  and  adits  shall  in  all 
cases  be  excavated  in  such  manner  and  to  such  dimensions  as 
will  give  suitable  room  for  the  necessary  timbering,  lining,  ven- 
tilating, pumping,  and  draining.    The  contractor  shall  use  every 
reasonable  precaution  to  avoid  excavating  beyond  the  outside 
lines  of  permanent  timbering  and  beyond  the  outside  neat  con- 
crete lines  where  no  permanent  timbering  is  required.     All 
drilling  and  blasting  shall  be  carefully  and  skilfully  done  so  as 
not  to  shatter  the  material  outside  of  the  required  lines.    Any 
blasting  that  would  probably  injure  the  work  will  not  be  per- 
mitted and  any  damage  done  to  the  work  by  blasting  shall  be 
repaired  by  the  contractor  at  his  expense,  and  in  a  manner  satis- 
factory to  the  engineer.    Tunnel  excavation  will  be  paid  for  at 
the  price  bid  per  linear  foot.    Partial  excavation,  as  in  the  case 
of  a  heading,  amounting  to  not  less  than  one-half  the  full  section, 
will  be  allowed  for  in  the  monthly  progress  estimates  at  one- 
fourth  of  the  price  named  in  the  contract  for  full  excavation. 

2.  Timbering. — Suitable  timbering  and  lagging  shall  be  used 
to  support  the  tunnel,  sides,  and  roof  wherever  necessary.     If 
practicable,  this  timbering  may  be  removed  before  the  construc- 
tion of  the  concrete  lining.     Timbering  may  be  left  in  place, 
provided  it  is  constructed  in  such  a  manner  as  not  to  weaken  the 
concrete  lining  and  is  in  accordance  with  designs  approved  by 
the  engineer.    An  approved  design  for  such  permanent  timbering 
is  shown  in  the  drawings,  but  in  case  this  design  is  found  to  be 
inadequate,  it  may  be  modified  from  time  to  time,  subject  to 
the  approval  of  the  engineer.     Lumber  for  timbering  shall  be 
furnished  by  the  contractor.    The  cost  of  furnishing  and  placing 
permanent  and  temporary  timbering  shall  be  included  in  the 


SPECIFICATIONS  335 

price  per  linear  foot  bid  in  the  schedule  for  excavating  the  tun- 
nel, except  that  in  addition  thereto  the  contractor  will  be  paid 
the  sum  of dollars  per  M  feet  B.  M.  for  permanent  timber- 
ing in  place.  No  payment  will  be  made  for  temporary  timbering 
nor  for  timber  used  in  filling  cavities.  In  measuring  permanent 
timbering  for  payment,  the  net  length  of  pieces  and  the  commer- 
cial cross-sectional  dimensions  will  be  taken.  Nothing  herein 
contained  shall  prevent  the  contractor  from  placing  such  tem- 
porary timbering  as  he  may  deem  necessary  nor  from  using  heav- 
ier permanent  timbering  than  that  shown  in  the  drawings,  nor 
shall  be  construed  to  relieve  the  contractor  from  sole  and  full 
responsibility  for  the  safety  of  the  tunnel  and  for  damage  to 
person  and  property. 

3.  Concrete  Lining. — The  tunnel  shall  be  lined  throughout 
with  concrete.     The  tunnel  lining  side  walls  and  arch,  where 
permanent  timbering  is  not  required,  shall  have  an  average 

thickness  of  ....  inches,  with  a  minimum  thickness  of inches 

over  projecting  points  of  rock.     The  average  thickness  of  the 

concrete  tunnel  invert  shall  be inches.    Where  permanent 

timber  is  required  it  shall  be  set  back  so  far  that  the  concrete 
lining  will  cover  the  timber  at  least  ....  inches.    The  concrete 
for  such  timbered  portions  of  the  tunnel  will  be  estimated  as 

having  an  average  thickness  of   inches.     If  the  tunnel  is 

excavated  to  greater  dimensions  than  necessary  for  placing  the 
prescribed  average  thickness  of  the  concrete  lining,  the  excess 
space  shall  be  solidly  filled  with  concrete,  or  the  lining  shall  be 
confined  with  forms  to  the  prescribed  thickness  and  properly 
backfilled.    Concrete  tunnel  lining  will  be  paid  for  by  the  cubic 
yard  at  the  unit  price  named  in  the  contract,  measured  to  the 
neat  lines  shown  in  the  drawings,  based  on  the  average  thickness 
herein  specified. 

4.  Lines  and  Grades. — The  contractor  shall  provide  such 
forms,  spikes,  nails,  troughs  for  plumb-bob  lines,  light,  etc.,  and 
such  assistance  as  may  be  required  by  the  engineer  in  giving 
lines  and  grades,  and  the  engineer's  marks  shall  be  carefully  pre- 
served.   Work  in  the  shafts,  adits,  and  tunnel  shall  be  suspended 
for  such  reasonable  time  as  the  engineer  may  require  to  transfer 
lines  and  to  mark  points  for  line  of  grade.     No  allowance  will 


336  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

be  made  to  the  contractor  for  loss  of  time  on  account  of  such 
suspension. 

5.  Draining. — The  contractor  shall  drain  the  tunnels  and 
adits  where  necessary  to  rid  the  same  of  standing  water.    Pump- 
ing shall  be  done  where  gravity  flow  to  an  outlet  cannot  be 
secured. 

6.  Lighting  and  Ventilating. — The  contractor  shall  properly 
light  and  ventilate  the  tunnel  during  construction. 

7.  Storage  and  Care  of  Explosives. — Caps  or  other  exploders 
or  fuses  shall  in  no  case  be  stored  or  kept  in  the  same  place  in 
which  dynamite  or  other  explosives  are  stored.     The  location 
and  design  of  powder  magazines,  methods  of  transporting  ex- 
plosives, and  in  general  the  precautions  taken  to  prevent  acci- 
dents must  be  satisfactory  to  the  engineer;  but  the  contractor 
shall  be  liable  for  all  damages  to  person  or  property  caused  by 
blasts  or  explosions. 

8.  Backfilling. — Any  space  outside  of  the  concrete  tunnel 
lining  shall  be  compactly  refilled  at  the  expense  of  the  contractor 
with  such  of  the  excavated  material  from  the  tunnel  as  may  be 
approved  by  the  engineer.    Large  cavities  in  the  tunnel  roof  may 
be  filled  with  waste  timber.     The  backfilling  to  the  springing 
lines  of  the  arch  shall  be  placed  before  the  arch  is  constructed, 
and  shall  be  brought  up  evenly  on  both  sides  of  the  tunnel;  it 
shall  be  spread  in  layers  not  exceeding  six  inches  in  thickness  and 
well  rammed.     The  invert  and  side  walls  shall  be  braced,  if 
required,  during  the  placing  of  the  backfilling. 

9.  Adits  and  Shafts. — The  contractor  shall  construct,  at  his 
own  expense,  such  adits  and  shafts  as  he  may  desire  to  use  to 
expedite  the  tunnel  work.    The  sides  and  the  arch  of  the  tunnel 
lining  situated  immediately  beneath  the  opening  of  each  shaft 
shall  be  increased  to  such  suitable  thickness  as  the  engineer 
may  prescribe;  and  each  adit  shall  be  closed  at  the  point  where 
it  meets  the  tunnel  with  a  block  of  concrete  averaging  at  least 
four  feet  in  thickness,  extending  into  the  sides  of  the  adit  two 
feet  and  having  a  foundation  two  feet  below  the  bottom  of  the 
tunnel.    All  concrete  required  for  this  purpose  shall  be  furnished 
by  the  contractor  at  his  own  expense,  the  cement  for  which  will 
be  furnished  to  the  contractor  at  its  cost  on  the  work.    All  shafts 


SPECIFICATIONS  337 

must  be  completely  refilled.  Dumping  from  the  top  will  not  be 
allowed  until  the  tunnel  arch  has  been  covered  to  a  depth  of  at 
least  ten  feet.  After  the  completion  of  the  block  of  concrete 
required  for  closing  an  adit,  the  adit  shall  be  refilled  and  the 
filling  tamped  into  place  for  a  distance  of  twenty  feet  from 
the  tunnel. 

SPECIFICATIONS  FOR  EXCAVATION  FOR  STRUCTURES 

1.  Excavation. — Unless  otherwise  shown  in  the  drawings, 
excavation  for  structures  will  be  measured  for  payment  to  lines 

outside  of  the  foundation  of  the 

structures  and   to  slopes  of ;  provided,  that, 

where  the  character  of  the  material  cut  into  is  such  that  it  can 
be  trimmed  to  the  required  lines  of  the  concrete  structure  and 
the  concrete  placed  against  the  sides  of  the  excavation  without 
the  use  of  intervening  forms,  payment  for  excavation  will  not  be 
made  outside  of  the  required  limits  of  the  concrete.    The  prices 
bid  for  excavation  shall  include  the  cost  of  all  labor  and  material 
for  cofferdams  and  other  temporary  structures  and  of  all  pump- 
ing, baling,  draining,  and  all  other  works  necessary  to  maintain 
the  excavation  in  good  order  during  construction. 

2.  Backfilling. — The  contractor  shall  place  and  shall  compact 
thoroughly  all  backfilling  around  structures.     The  compacting 
must  be  equivalent  to  that  obtained  by  the  tramping  of  well- 
distributed  scraper  teams  depositing  the  material  in  layers  not 
exceeding  six  inches  thick  when  compacted.      The  material  used 
for  this  purpose,  the  amount  thereof,  and  the  manner  of  deposit- 
ing the  same  must  be  satisfactory  to  the  engineer.     So  far  as 
practicable,  the  material  moved  in  excavating  for  structures  shall 
be  used  for  backfilling,  but  when  sufficient  suitable  material  is 
not  available  from  this  source,  additional  material  shall  be  ob- 
tained from  borrow  pits  selected  by  the  engineer.    Payment  for 
backfilling  will  be  made  at  the  price  per  cubic  yard  bid  therefor 
in  the  schedule. 

3.  Puddling. — Backfilling  and  embankment  around  struc- 
tures within  ....  feet  of  the  structure  shall  be  made  with  material 
approved  by  the  engineer,  and  where  practicable  shall  consist  of 
sand  and  gravel,  with  an  admixture  of  clay  equal  to  one-fourth 


338  WORKING    DATA   FOR    IRRIGATION   ENGINEERS 

to  one-half  the  volume  of  the  sand  and  gravel.  The  material 
shall  be  deposited  in  water  of  such  depth  as  is  approved  by  the 
engineer,  unless  the  quantity  of  clay  predominates,  in  which 
case  the  engineer  may  in  his  discretion  order  the  material  depos- 
ited in  layers  of  six  inches  or  less,  and  compacted  by  tamping  or 
rolling  with  the  smallest  quantity  of  water  that  will  insure  con- 
solidation. Payment  for  the  work  specified  in  this  paragraph 
will  be  made  at  the  unit  price  bid  for  puddling,  and  will  be  in 
addition  to  the  payment  made  for  excavation  and  overhaul. 

4.  Blasting. — Any  blasting  that  will  probably  injure  the  work 
will  not  be  permitted  and  any  damage  done  to  the  work  by 
blasting  shall  be  repaired  by  the  contractor  at  his  expense. 

SPECIFICATIONS  FOR  CONTINUOUS  WOOD 
STAVE  PIPE 

1.  Description. — The  pipe  shall  be  of  the  continuous-stave 
metal-banded  type  with  metal  tongues  driven  into  slots  in  the 
ends  of  the  staves  to  form  the  butt  joints.    The  alignment  and 
profile  of  the  pipe  are  shown  in  the  drawings.     Each  proposal 
shall  be  accompanied  by  drawings  showing  clearly  detail  dimen- 
sions of  staves,  bands,  and  tongues,  which  shall  comply  with  the 
requirements  of  the  specifications.     Omission  of  drawings  from 
proposals  or  any  uncertainty  as  to  detail  dimensions  will  be 
sufficient  cause  for  rejection. 

2.  Material. — All  material  of  whatever  nature  required  in 
the  work  shall  be  furnished  by  the  contractor.    The  price  bid  for 
wood  staves  in  place  shall  include  the  cost  of  all  necessary  tongues, 
and  all  royalties  for  special  material  or  devices  used  in  the  pipe 
or  in  its  construction.     The  price  bid  for  bands  in  place  shall 
include  all  necessary  shoes  and  fastenings  and  asphaltum  coat- 
ing, and  all  royalties  for  special  devices  used  in  the  pipe  or  in 
its  construction. 

3.  Diameter  of  Pipe. — The  inside  diameter  of  the  pipe  shall 
be  ....  inches,  measured  after  completion  of  the  work.    No  di- 
ameter at  any  point  shall  differ  more  than  !}/£  per  cent  from  the 
average  diameter  of  the  pipe  at  said  point,  and  the  average  of 
the  vertical  and  horizontal  diameters  at  any  point  shall  not  be 
less  than  the  specified  diameter. 


SPECIFICATIONS  339 

4.  Staves. — All  lumber  used  in  staves  shall  be  Douglas  fir 
or  redwood.    It  shall  be  sound,  straight-grained,  and  free  from 
dry-rot,  checks,  wind  shakes,  wane,  and  other  imperfections 
that  may  impair  its  strength  or  durability.     Redwood  shall  be 
clear  and  free  from  sap.    In  Douglas  fir  sap  will  not  be  allowed 
on  more  than  10  per  cent  of  the  inside  face  of  any  stave  and  in 
not  more  than  10  per  cent  of  the  total  number  of  pieces;  sap 
shall  be  bright  and  shall  not  occur  within  4  inches  of  the  ends  of 
any  piece;  pitch  seams  will  be  permitted  in  not  over  10  per  cent 
of  the  total  number  of  pieces,  if  showing  on  the  edge  only,  and 
if  not  longer  than  4  inches  nor  wider  than  /(e  inch;  no  through 
knots  or  knots  at  edges  nor  within  6  inches  of  ends  of  staves 
will  be  allowed;  sound  knots  not  exceeding  J/2  inch  in  diameter, 
not  falling  within  the  above  limitations,  nor  exceeding  three 
within  a  10-foot  length  will  be  accepted.     All  lumber  used  shall 
be  seasoned  by  not  less  than  60  days'  air  drying  in  open  piles 
before  milling  or  by  thorough  kiln  drying.    All  staves  shall  have 
smooth-planed  surfaces  and  the  inside  and  outside  faces  shall  be 
accurately  milled  to  the  required  circular  arcs  to  fit  a  standard 
pattern  provided  by  the  contractor.     Staves  shall  be  trimmed 
perfectly  square  at  ends  and  the  slots  for  tongues  shall  be  in 
exactly  the  same  relative  position  for  all  ends  and  according  to 
detail  drawings  furnished  by  the  contractor.    Staves  shall  have 
an  average  length  of  not  less  than  15  feet  6  inches  and  not  more 
than  1  per  cent  of  the  staves  shall  have  a  length  of  less  than 
9  feet  6  inches.    No  staves  shorter  than  8  feet  will  be  accepted. 

The  finished  thickness  of  staves  shall  not  be  less  than inches. 

All  staves  delivered  on  the  work  in  a  bruised  or  injured  condition 
will  be  rejected.    If  staves  are  not  immediately  used  on  arrival 
at  the  site  of  the  work,  they  shall  be  kept  under  cover  until  used. 

5.  Bands. — A  band  shall  consist  of  one  complete  fastening 
and  shall  include  the  bolts,  shoes,  nuts,  and  washers  necessary 
to  form  same. 

6.  Band  Spacing. — The  distance  center  to  center  of  bands 
shall  be  as  marked  on  the  profile,  except  that  where  the  spacing 
as  marked  is  such  as  to  make  the  distances  from  bands  to  the 
ends  of  staves  more  than  4  inches,  extra  bands  shall  be  used 
to  keep  such  distances  within  4  inches. 


340  WORKING    DATA    FOR    IRRIGATION    ENGINEERS 

7.  Bolts. — All  bolts  shall  be  of  ....  inch  diameter  steel  and 
shall  conform  to  the  following  specifications:    (see  specifications 
for  structural  steel).     Bolts  may  have  either  button  or  bolt 
heads.    They  shall  be  at  least  as  strong  in  thread  as  in  body,  and 
threads  shall  permit  the  nut  to  run  freely  the  entire  length 
of  thread.    Nuts  shall  be  of  such  thickness  as  to  insure  against 
stripping  of  threads. 

8.  Shoes. — There  shall  be  ....  malleable  iron  shoes  to  each 
band.     ( Note:    It  is  customary  to  use  only  one  shoe  for  pipe  48 
inches  and  smaller  in  diameter  and  two  shoes  for  larger  sizes. 
For  very  large  pipe  more  than  two  may  be  necessary.)     Shoes 
shall  fit  accurately  to  the  outer  surface  of  the  pipe  and  shall 
have    the    dimensions    shown    on    the    drawing,    or    the    con- 
tractor may  submit  for  approval  a  drawing  or  sample  of  some 
other  type  of  shoe  which  he  may  desire  to  furnish.    If  required, 
such  shoe  shall  be  shown  under  suitable  test  to  be  stronger  than 
the  bolt.    The  material  for  shoes  shall  conform  to  the  following 
specifications :    (see  standard  specifications  for  malleable  castings) . 

9.  Tongues. — Shall  be  of  galvanized  steel  or  iron inch 

thick  and  ....  wide.    Their  length  shall  be  such  that  when  in 
place,  they  will  penetrate  into  the  sides  of  the  adjacent  staves 
without  undue  injury.    The  tongues  and  slots  shall  be  so  pro- 
portioned as  to  insure  a  tight  fit  of  the  tongues  into  the  slots 
without  danger  of  splitting  the  staves. 

10.  Coating  of  Bands. — The  bands  shall  be  coated  by  being 
dipped  when  hot  in  a  mixture  of  pure  California  asphalt,  or 
equivalent.    Bolts  shall  be  bent  to  the  required  arc  before  dip- 
ping.   If  the  bands  are  dipped  cold  they  shall  be  left  in  the  hot 
bath  a  sufficient  length  of  time  to  insure  that  they  have  acquired 
the  temperature  of  the  asphalt.    This  coating  shall  be  so  pro- 
portioned and  applied  that  it  will  form  a  thick  and  tough  coating 
free  from  tendency  to  flow  or  become  brittle  under  the  range  of 
temperature  to  which  it  will  be  subjected.     Where  the  pipe  is 
uncovered  and  exposed  to  the  full  range  of  atmospheric  temper- 
atures, not  less  than  7  per  cent  and  not  more  than  10  per  cent  of 
pure  linseed  oil  shall  be  mixed  with  the. asphalt. 

11.  Erection. — The  pipe  shall  be  built  in  a  workmanlike 
manner.    The  ends  of  adjoining  staves  shall  break  joint  at  least 


SPECIFICATIONS  341 

3  feet.  The  staves  shall  be  driven  in  such  a  manner  as  to  avoid 
any  tendency  to  cause  wind  in  the  pipe  and  the  required  grade 
and  alignment  must  be  maintained.  Staves  shall  be  well  driven 
to  produce  tight  butt  joints;  driving  bars,  or  other  suitable  means 
being  used  to  avoid  marring  or  damaging  staves  in  driving.  In 
rounding  out  the  pipe,  care  shall  be  exercised  to  avoid  damage 
by  chisels,  mauls,  or  other  tools.  The  pipe  shall  be  rounded  out 
to  produce  smooth  inner  and  outer  surfaces.  Bands  shall  be 
accurately  spaced  and  placed  perpendicular  to  the  axis  of  the 
pipe.  Shoes  shall  be  placed  so  as  to  cover  longitudinal  joints 
between  staves  and  bear  equally  on  two  staves  as  nearly  as 
practicable.  They  shall  be  placed  alternately  on  opposite  sides 
of  the  pipe,  so  as  to  be  out  of  line  and  cover  successively  on  each 
side  at  least  three  joints.  Shoes  shall  not  be  allowed  to  cover 
the  butt  joints.  Bolts  shall  be  hammered  thoroughly  into  the 
wood  to  secure  a  bearing  on  60°  of  the  circumference  of  the 
bolt.  All  kinks  in  bolts  shall  be  carefully  hammered  out. 
Bands  shall  be  back-cinched  to  the  satisfaction  of  the  engineer 
so  as  to  produce  the  required  initial  compressive  stresses  in  the 
staves.  All  metal  work  shall  be  handled  with  reasonable  care 
so  as  to  avoid  injury  to  the  coating  as  much  as  possible.  In 
hammering  shoes  into  place  they  shall  be  struck  so  as  to  avoid 
deformation  or  injury.  After  erection  the  contractor  shall 
retouch  all  metal  work,  where  abraded,  with  an  asphaltum  paint 
satisfactory  to  the  engineer. 

12.  Painting. — After  erection  and  while  the  pipe  is  dry  the 
entire  outer  surface  shall  be  given  a  coat  of  refined  water-gas 
tar,  followed  by  a  coat  of  refined  coal-gas  tar,  thinned  with  dis- 
tillate, applied  with  brushes  or  sprayed  on  with  air  pressure. 
Before  application  of  the  paint  the  surface  of  the  pipe  shall  be 
thoroughly  cleaned  of  dirt,  dust,  and  foreign  matter  of  every 
kind.    All  checks,  cracks,  and  surface  irregularities  of  every  kind 
shall  be  thoroughly  filled  with  paint.    The  finished  thickness  of 
the  coating  shall  be  not  less  than  /(6  inch.    The  cost  of  all  work 
under  this  paragraph  shall  be  included  in  the  price  bid  for  pipe 
in  place.     (Note:    Redwood,  not  painted,  is  probably  equal  in 
durability  to  Douglas  fir  painted.) 

13.  Inspection. — Final  inspection  of  materials,  as  well  as 


342  WORKING  DATA   FOR  IRRIGATION  ENGINEERS 

erection,  will  be  made  on  the  work,  but  if  the  contractor  so  de- 
sires, preliminary  inspection  of  staves  may  be  made  at  the  mill 
at  the  contractor's  expense.  Mill  inspection,  however,  shall  not 
operate  to  prevent  the  rejection  of  any  faulty  material  on  the 
work.  Tests  of  metal  work  will  be  made  at  the  point  of  manu- 
facture by at own  expense;  or  they  may 

be  made  at  the  plant  by  the  contractor  or  his  employees  acting 
under  the  direction  of  the  engineer  or  his  representative;  or  cer- 
tified tests  may,  at  the  option  of  the  engineer,  be  accepted  in  lieu 
of  the  above-mentioned  tests.  The  contractor  shall  provide,  at 
his  own  expense,  the  necessary  test  pieces,  and  shall  notify  the 
engineer  or  his  representatives  when  these  pieces  are  ready  for 
testing.  All  test  bars  and  test  pieces  shall  be  marked  so  as  to 
indicate  clearly  the  material  that  they  represent,  and  shall  be 
properly  boxed  and  prepared  for  shipment  if  required. 

14.  Tests  of  Pipe. — On  completion  of  the  work,  or  as  soon  as 
possible  thereafter,  the  contractor  shall  make  a  full  pressure 
test  of  the  pipe.    All  leaks  found  at  the  time  of  the  test  shall  be 
made  tight  by  the  contractor.    If  the  leakage  is  not  so  large  as 
to  endanger  the  foundation  of  the  pipe,  the  pipe  shall  be  kept 
under  full  pressure  for  two  days  before  plugging  of  leaks  is 
started  in  order  to  allow  the  wood  to  become  thoroughly  satu- 
rated.   The  cost  of  making  the  test  shall  be  borne  by  the  con- 
tractor. 

15.  Payments. — 

SPECIFICATIONS  FOR  MANUFACTURE  OF  MACHINE- 
BANDED  WOOD  STAVE  PIPE 

1.  Description. — The  pipe  shall  be  of  the  jointed,  wood- 
stave,  machine-banded  type. 

2.  Lengths  of  Pipe  Sections. — Pipe  shall  be  furnished  in 
lengths  of  10  to  20  feet  and  the  average  length  shall  be  not  less 
than  16  feet.    Shorter  sections  shall  be  furnished  only  if  required 
for  making  sharp  curves,  in  which  case  the  lengths  shall  not  be 
more  than  one  foot  shorter  than  will  be  required  to  keep  the 
joint  opening  at  the  outside  of  the  curve  due  to  throw  within 
a  limit  of  /{6  inch. 

3.  Material. — All  material  of  whatever  nature  required  in 


SPECIFICATIONS  343 

the  manufacture  of  the  pipe  in  accordance  with  these  specifica- 
tions shall  be  furnished  by  the  contractor. 

4.  Diameters  of  Pipes. — The  diameters  of  pipes  shall  be  as 
listed  in  the  schedules.     No  diameter  of  any  pipe  shall  differ 
more  than  1  per  cent  from  the  specified  diameter  of  the  pipe,  and 
the  average  of  the  vertical  and  horizontal  diameters  at  any  point 
shall  not  be  less  than  the  specified  diameter. 

5.  Thickness  of  Staves. — The  finished  thickness  of  staves 
shall  be  as  follows : 


4"  to  6" l  1/16 

8"  to  10" 1  1/8 

12"  to  14" 1  3/16 

16"  to  18" 1  1/4 

20"  to  24" 1  5/16 


6.  Lumber  for  Staves. — All  lumber  used  in  staves  shall  be 
Douglas  fir  or  redwood.    It  shall  be  sound,  straight-grained,  and 
free  from  dry-rot,  checks,  wind  shakes,  wane,  and  other  imper- 
fections that  may  impair  its  strength  or  durability.    Redwood 
shall  be  clear  and  free  from  sap.    In  the  Douglas  fir  sap  will  not 
be  allowed  on  more  than  10  per  cent  of  the  inside  face  of  any 
stave,  and  in  not  more  than  10  per  cent  of  the  total  number  of 
pieces;  sap  shall  be  bright  and  shall  not  occur  within  4  inches  of 
the  ends  of  any  piece;  pitch  seams  will  be  permitted  in  not  over 
10  per  cent  of  the  total  number  of  pieces,  if  showing  on  the  edge 
only,  and  if  not  longer  than  4  inches  nor  wider  than  /{6  inch;  no 
through  knots  nor  knots  at  edges  nor  within  6  inches  of  ends  of 
staves  will  be  allowed;  sound  knots  not  exceeding  J^  inch  in 
diameter,  not  falling  within  the  above  limitations,  nor  exceeding 
three  within  a  10-foot  length,  will  be  accepted.    All  lumber  used 
shall  be  seasoned  by  not  less  than  sixty  days'  air  drying  in  open 
piles  before  milling  or  by  thorough  kiln  drying.     All  staves 
shall  have  smooth-planed  surfaces,  and  the  inside  and  outside 
faces  shall  be  accurately  milled  to  the  required  circular  arcs. 

7.  Banding. — Size  and  spacing  of  banding  wire  shall  be 
designed  for  a  working  stress  of  12,000  pounds  per  square  inch 
on  the  wire.    The  spacing  shall  in  no  case  be  greater  than  4 
inches,  center  to  center  of  wires,  nor  greater  than  will  produce  a 


344  WORKING    DATA    FOR    IRRIGATION    ENGINEERS 

pressure  of  wire  on  the  wood  of  800  pounds  per  square  inch  as 

pRf 

calculated  from  the  formula  B  =  —TIT where  B  =  pressure 

r  (JK.+  t) 

on  wood  in  pounds  per  square  inch;  p  =  water  pressure  in 
pounds  per  square  inch;/  =  spacing  of  wire  in  inches;  R  =  in- 
side radius  of  pipe  in  inches;  r  =  radius  of  wire  in  inches;  and 
/  =  thickness  of  staves  in  inches.  No  wire  smaller  than  No.  8 
United  States  Standard  gage  shall  be  used.  Wire  shall  be  of 
medium  steel  with  a  tight  coating  of  galvanizing  and  shall 
have  an  ultimate  tensile  strength  of  55,000  to  65,000  pounds 
per  square  inch,  and  capability  of  being  bent  flat  on  itself 
without  fracture.  The  galvanizing  shall  pass  the  standard 
test  of  four  immersions  in  a  standard  solution  of  copper 
sulphate  and  shall  show  no  lumps  of  zinc.  The  bidder  shall 
state  in  his  proposal  the  size  of  banding  wire  he  proposes  to 
furnish. 

8.  Joints. — Inserted  joint  pipe  shall  be  furnished  for  diam- 
eters of  12  inches  and  less  and  for  heads  not  exceeding  50  feet. 
For  pipes  of  larger  diameter  than  12  inches,  and  for  all  pipes 
under  more  than  50  feet  head,  wood  sleeve  collars  shall  be  fur- 
nished.   The  banding  on  collars  shall  be  50  per  cent  stronger 
than  the  banding  on  the  pipe. 

9.  Individual  Bands. — Individual  bands  shall  be  used  on  all 
collars  for  pipe  12  inches  and  greater  in  diameter.    The  smallest 
bolts  used  shall  be  Y%  mch  m  diameter.    The  bolt  shall  have  an 
ultimate  tensile  strength  of  55,000  to  65,000  pounds  per  square 
inch;  an  elastic  limit  of  one-half  the  ultimate  tensile  strength, 
and  capability  of  being  bent  back  flat  on  itself  without  fracture. 
The  shoes  shall  be  malleable  iron,  and  shall  be  stronger  than  the 
bolts,  with  sufficient  bearing  on  the  wood  at  the  tail  to  prevent 
injurious  indentation  in  cinching.    The  shoes  shall  be  sound  and 
free  from  blow-holes,  and  shall  have  an  ultimate  tensile  strength 
of  not  less  than  40,000  pounds  per  square  inch.    Bidders  shall 
submit  samples  or  drawings  of  the  type  of  shoe  they  propose  to 
furnish. 

10.  Coating. — After  manufacture  the  outside  of  the  pipe  and 
collars  shall  be  dipped  in  a  bath  of  hot  coal  tar  and  asphaltum. 
Previous  to  dipping  the  collars  in  coal  tar  and  asphaltum  they 


SPECIFICATIONS 


345 


shall  be  dipped  for  a  depth  of  1  inch  at  each  end  for  a  period  of 
ten  minutes  in  a  bath  of  creosote.  Care  should  be  exercised  to 
keep  the  coal  tar  and  asphaltum  from  the  tenon  ends  and  inside 
surfaces,  and,  if  necessary,  the  tenons  shall  be  wrapped  with 
paper  while  being  dipped.  After  dipping,  the  pipe  and  collars 
shall  be  rolled  in  fine  sawdust  while  the  coating  is  still  soft. 

11.  Inspection. — Inspection  of  pipe  will  be  made  at  the  mill, 
but  the  manufacturer  will  be  held  responsible  for  any  damage 
in  transit  caused  by  improper  loading  of  the  pipe. 

12.  Marking. — Each  section  of  pipe  shall  be  plainly  marked 
on  the  inside  at  one  end,  showing  the  head  for  which  the  section 
was  wound,  and  the  number  of  the  banding  wire  used. 

13.  Shipment. — 

14.  Payment. — 

SPECIFICATIONS  FOR  STEEL  PIPE 

1.  Description. — Steel  pipe  may  be  either  of  the  lockbar  or 

riveted  steel  type.     Riveted  steel  shall  have  \  1  courses. 

[     taper     J 

Circular  seams  may  be  single-riveted  and  longitudinal  seams 

shall  be  \  .n*V     <*  riveted.    The  bidder  shall  submit  with  his  bid 
[  double  J 

a  drawing  showing  details  of  joints,  size  and  spacings  of  rivets, 
etc.  Failure  to  submit  such  drawing  will  be  sufficient  cause  for 
rejection  of  the  bid. 

2.  Thickness  of  Metal. — The  thickness  of  steel  sheets  shall 
be  as  follows: 


Length, 
Feet 

THICKNESS, 
INCHES 

Head, 
Feet 

Riveted 

Lockbar 

346  WORKING  DATA   FOR   IRRIGATION  ENGINEERS 

3.  Planing   and   Scarfing. — When   necessary   the   edges   of 
plates  shall  be  prepared  for  caulking  by  planing  and  scarfing  at 
the  factory. 

4.  Riveting. — The  riveting  and  other  details  of  longitudinal 
seams  shall  be  designed  to  withstand  the  heads  given  in  para- 
graph 2.    The  rivets  for  circular  joints  shall  be  of  the  same 
size  as  for  longitudinal  seams.    The  intensity  of  working  stress 
on  rivets  shall  be  7,500  pounds  per  square  inch  in  shear  and 
15,000  pounds  per  square  inch  in  bearing  on  riveted  plates.    All 
rivet  spacing  shall  be  arranged  to  give  the  greatest  possible 
efficiency  of  joint.    Size  of  rivets  and  rivet  spacing  shall  be  sub- 
mitted to  the  engineer  for  approval.    All  riveting  shall  be  done 
in  the  field,  but  sufficient  of  the  work  done  with  different  tem- 
plates must  be  assembled  at  the  shop  to  prove  the  work  correct. 
(When  appropriate,  shop  riveting  should  be  specified.) 

5.  Punching. — Rivet  holes  may  be  punched  and  shall  be  no 
larger  than  is  necessary  to  pass  the  required  size  of  rivet.    Drift 
pins  shall  not  be  used  except  for  bringing  together  the  several 
parts,  and  drifting  with  such  force  as  to  distort  the  holes  will  not 
be  allowed.    Wrongly  punched  plates  shall  not  be  corrected  by 
plugging  the  holes  and  re-punching,  but  shall  be  rejected.    All 
burrs  and  ragged  edges  on  plates  shall  be  smoothed  off  before 
the  material  leaves  the  shop.    All  punching  shall  be  done  at  the 
shop  before  shipment. 

6.  Material. — All  steel  shall  be  made  by  the  open-hearth 
process.    Steel  for  plates  shall  be  of  the  grade  known  as  "  boiler 
plate."    Steel  for  rivets  shall  be  of  the  grade  known  as  "  boiler 
rivet  steel." 

7.  Chemical  and  Physical  Properties  of  Boiler  Plate  Steel.— 
Boiler  plate  steel  shall  contain  not  more  than  .05  per  cent  phos- 
phorus, .05  per  cent  sulphur,  and  from  0.30  to  0.60  per  cent 
manganese.    It  shall  show  an  ultimate  tensile  strength  of  55,000 
to  65,000  pounds  per  square  inch;  an  elastic  limit  of  not  less  than 
one-half  the  ultimate  tensile  strength;  an  ultimate  elongation  in 
8  inches  of  not  less  than  1,500,000  divided  by  the  ultimate 
tensile  strength;  and  capability  of  being  bent,  cold  or  quenched, 
180°  flat  without  fracture.    The  steel  shall  be  in  all  respects  such 
as  to  stand  punching,  caulking,  and  riveting  without  showing  the 


SPECIFICATIONS  347 

least  tendency  to  crack.  Plates  shall  withstand,  without  crack- 
ing of  the  material,  a  drift  test  made  by  driving  a  pin  into  a 
%-inch  hole,  enlarging  same  to  a  diameter  of  1  inch.  In  all 
respects  not  covered  in  these  specifications  boiler  plate  steel 
shall  conform  to  the  "  Standard  Specifications  for  Boiler  Steel  " 
of  the  American  Society  for  Testing  Materials,  adopted  Aug- 
ust 25,  1913. 

8.  Chemical  and  Physical  Properties  of  Rivet  Steel. — Steel 
for  rivets  shall  contain  not  more  than  .04  per  cent  of  phosphorus, 
.045  per  cent  sulphur,  and  from  0.30  to  0.50  per  cent  of  man- 
ganese.   It  shall  show  an  ultimate  tensile  strength  of  45,000  to 
55,000  pounds  per  square  inch;  an  elastic  limit  of  not  less  than 
one-half  the  ultimate  tensile  strength;  an  ultimate  elongation  in 
8  inches  of  not  less  than  1,500,000  divided  by  the  ultimate  tensile 
strength,  but  need  not  exceed  30  per  cent;  and  capability  of  being 
bent,  cold  or  quenched,  180°  flat  without  fracture.    Rivet  rounds 
shall  be  tested  of  full  size  as  rolled.    In  all  respects  not  covered 
in  these  specifications  steel  for  rivets  shall  conform  to  the  "  Stand- 
ard Specifications  for  Boiler  Rivet  Steel "   of  the  American 
Society  for  Testing  Materials,  adopted  August  25,  1913. 

9.  Marking.— Each  plate  shall  be  distinctly  stamped  with 
its  melt  or  slab  number.    Rivet  steel  may  be  shipped  in  securely 
fastened  bundles  with  melt  number  stamped  on  a  metal  tag 
attached.    Plates  and  other  parts  shall  be  plainly  marked  for 
identification  and  assembly  in  the  field. 

10. — Test  Pieces. — (This  paragraph  should  state  who  is  to 
furnish  test  pieces,  what  disposition  shall  be  made  of  broken  test 
specimens,  etc.) 

n.  Tests  of  Material. — (This  paragraph  should  state  who  is 
to  make  tests,  at  whose  expense  tests  are  to  be  made,  etc.) 

12.  Shipment. — 

13.  Erection. — Erection  of  pipe  shall  be  commenced  at  the 
point  directed  by  the  engineer.     The  contractor  shall  haul  all 
material  and  distribute  same  along  the  trench  and  shall  furnish 
a  compressed-air  plant  and  full  equipment .  for  air  riveting,  and 
all  other  equipment,  tools,  and  supplies  required  for  the  erection 
of  the  pipe  and  completion  for  service.    The  pipe  shall  be  care- 
fully caulked  and  painted  as  the  work  progresses.    The  work  of 


348  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

assembling,  riveting,  and  caulking  shall  be  done  by  workmen 
experienced  in  this  line.  Riveting  shall  show  first-class  workman- 
ship, rivet  heads  shall  be  full  and  concentric  with  the  body  of 
the  rivet,  and  the  rivet  shall  completely  fill  the  hole  and  thor- 
oughly pinch  the  connected  pieces  together.  Rivets  that  are 
loose  or  have  defective  heads  shall  be  removed  and  other  rivets 
substituted  therefor. 

14.  Painting. — Inside  and  outside  of  pipe  shall  be  covered 
with  three  coats  of  a  reliable  brand  of  asphalt  paint  which  shall 
be  subject  to  the  approval  of  the  engineer.    Before  painting  all 
surfaces  shall  be  thoroughly  cleaned  by  scrubbing  with  wire 
brushes  or  other  means  as  directed  by  the  engineer.    All  riveted 
joints  shall  be  painted  before  riveting.    All  paint  shall  be  applied 
while  the  pipe  is  warm  and  thoroughly  dry. 

15.  Defective  Work. — The  contractor  shall  guarantee  the 
material  and  workmanship  furnished  by  him  to  be  free  from 
defects  of  material  and  construction,  and  he  shall  replace  free 

of  cost  to    any  material  that  shall  develop 

faults  during  construction  or  tests. 

1 6.  Test  of  Pipe. — On  completion  of  erection,  or  as  soon  as 
possible  thereafter,  the  contractor  shall  make  a  full-pressure  test 
of  the  pipe.    The  pipe  shall  be  water-tight  under  this  test  and 
the  contractor  shall  correct  any  defects  that  develop. 

17.  Payments.— 

SPECIFICATIONS  FOR  JOINTED  REINFORCED  CON- 
CRETE PIPE 

1.  Description. — The  pipe  shall  be  composed  of  concrete 
reinforced  with  steel  rods  or  wire  and  built  in  vertical  forms  in 
lengths  of  ....  feet;  the  sections  being  connected  in  the  trench 
by  concrete  collars  reinforced  with  steel. 

2.  Diameter  of  Pipe. — The  inside  diameter  of  the  pipe  shall 

be inches  and  no  diameter  shall  differ  more  than  0.5  per 

cent  from  the  specified  diameter  of  the  pipe.    Each  section  of 
pipe  shall  be  a  true  right  cylinder  with  the  plane  of  the  ends 
perpendicular  to  the  axis  of  the  pipe. 

3.  Thickness  of  Shell. — The  shell  of  the  pipe  shall  have  a 
thickness  of          ,   inches  which  shall  be  uniform  around  the 


SPECIFICATIONS  349 

entire  circumference.    In  no  case  will  a  variation  of  more  than 
10  per  cent  from  the  specified  thickness  be  allowed. 

4.  Manufacture. — The  concrete  shall  be  thoroughly  mixed 
in  a  mechanical  batch  mixer.     It  shall  be  deposited  in  such  a 
manner  that  no  separation  of  ingredients  will  occur  and  suitable 
tools  shall  be  used  to  settle  the  concrete  thoroughly  and  produce 
smooth  surfaces.     Great  care  shall  be  exercised  to  maintain 
proper  spacing  of  the  reinforcing  rods.    No  pipe  shall  be  manu- 
factured when  the  temperature  of  the  atmosphere  is  above  90°, 
except  by  permission  of  the  engineer.    During  manufacture  the 
concrete  and  forms  shall  be  protected  from  the  direct  rays  of  the 
sun,  and  thereafter  the  sections  shall  be  kept  covered  for  five 
days  and  they  shall  be  kept  moist  for  twenty  days.     Manufac- 
ture shall  not  be  carried  on  in  freezing  weather,  except  in  a 
heated  enclosure,  and  the  sections  of  pipe  shall  be  prevented 
from  freezing.    Immediately  after  removal  of  the  forms  all  de- 
fects in  the  surface  of  the  concrete  shall  be  smoothed  up  with  a 
1  to  1  mixture  of  cement  and  fine  sand,  especial  care  being  taken 
to  produce  smooth  interior  surfaces.    Forms  shall  not  be  removed 
in  less  than  twenty-four  hours  after  the  concrete    has  been 
poured. 

5.  Forms. — The  forms  used  shall  be  subject  to  the  approval 
of  the  engineer.     All-steel  forms  are  preferred,   but  wooden 
forms  with  steel  linings  may  be  used,   provided  the  desired 
results  can  be  obtained  therewith.    Forms  shall  be  strong  and 
rigid  with  sufficient  bracing  to  prevent  warping  in  handling,  or 
pouring  concrete.    They  shall  be  provided  with  suitable  attach- 
ments for  making  the  joint  grooves  at  the  ends  in  accordance 
with  the  drawings.    A  sufficient  number  of  forms  shall  be  pro- 
vided to  allow  the  manufacture  of  not  less  than  ....  sections  of 
pipe  per  day,  or  such  additional  number  as  may  be  necessary  to 
complete  the  work  within  the  specified  time. 

6.  Reinforcement. — The  transverse  reinforcement  shall  con- 
sist of  medium  steel  rods  or  wire  and  shall  be  spaced  as  shown 
on  the  drawings.    Sufficient  longitudinal  reinforcement  shall  be 
used  to  fasten  the  transverse  rods  and  hold  them  rigidly  in  place. 
The  transverse   reinforcement  may  be  either  individual  rods, 
welded  or  lapped  and  wired  at  the  ends  for  a  length  of  24  di- 


350  WORKING  DATA  FOR  IRRIGATION   ENGINEERS 

ameters,  or  it  may  be  wound  in  helical  coils.    The  latter  method 
is  preferred  where  its  use  is  practicable. 

7.  Steel. — Steel  may  be  made  by  either  the  open-hearth  or 
Bessemer  process.    It  shall  contain  not  more  than  0.1  per  cent 
phosphorus  if  made  by  the  Bessemer  process,  and  not  more  than 
0.05  per  cent  if  made  by  the  open-hearth  process.    It  shall  have 
an  ultimate  tensile  strength  of  55,000  to  70,000  pounds  per 
square  inch;  an  elastic  limit  not  less  than  33,000  pounds  per 
square  inch;  a  minimum  per  cent  of  elongation  in  8  inches  of 
1,400,000  divided  by  the  ultimate  tensile  strength;  and  capability 
of  being  bent  cold  without  fracture  180°  around  a  pin  having 
a  diameter  equal  to  the  thickness  of  the  test  piece.      Bars  or 
wire  will  be  subject  to  rejection  if  the  actual  weight  of  any  lot 
varies  more  than  5  per  cent  over  or  under  the  theoretical  weight 
of  that  lot. 

8.  Concrete. — Concrete  shall  be  composed  of  cement,  sand, 
and  gravel,  well  mixed  and  brought  to  a  proper  consistency  by 
the  addition  of  water.    The  proportions  will  depend  upon  the 
nature  of  component  materials  and  upon  the  head  of  water  that 
the  pipe  will  be  subjected  to,  but  will  vary  in  general  from  one 
part  cement  to  five  parts  aggregate,  to  one  part  cement  to 
six  parts  aggregate.    The  contractor  shall  not  be  entitled  to 
any  extra  compensation  by  reason  of  such  variations.     (Note: 
If  the  contractor  furnisfos  the  cement  this  paragraph  must   be 
modified  so    as    to    provide    for    separate    prices  for    different 
mixtures.} 

9.  Cement. — * 

10.  Sand. — Sand  for  concrete  shall  be  obtained  from  natural 
deposits.     The  particles  shall  be  hard,  dense,  durable,  non- 
organic  rock  fragments,  such  as  will  pass  a  )^-inch  mesh  screen. 
The  sand  must  be  free  from  organic  matter  and  must  contain 
not  more  than  3  per  cent  of  clayey  material  or  other  objectionable 
non-organic  matter.    The  sand  must  be  so  graded  that,  when 
dry  and  well  shaken,  its  voids  will  not  exceed  35  per  cent. 

n.  Gravel. — Gravel  for  concrete  shall  consist  of  hard,  dense, 
durable  rock  pebbles  that  will  pass  through  a  ....  inch  mesh 
screen  and  that  will  be  rejected  by  a  %-mch  rnesh  screen. 
(Note:  Gravel  is  better  suited  for  thin-shelled  reinforced  concrete 


SPECIFICATIONS  351 

pipe  on  account  of  the  greater  ease  with  which  it  can  be  worked  in 
around  the  reinforcement.) 

12.  Water. — The  water  used  in  mixing  concrete  shall  be 
reasonably   clean,   and   free  from   objectionable   quantities   of 
organic  matter,  alkali,  salts,  and  other  impurities. 

13.  Mixing  Concrete. — The  cement,  sand,  and  gravel  shall 
be  so  mixed  and  the  quantities  of  water  added  shall  be  such  as 
to  produce  a  homogeneous  mass  of  uniform  consistency.     Dirt 
and    other    foreign    substances    shall    be    carefully    excluded. 
Machine  mixing  will  be  required,  and   the  machine  and  its 
operation  shall  be  subject  to  the  approval  of  the  engineer. 
Enough  water  shall  be  used  to  give  the  concrete  a  mushy 
consistency.    If  concrete  is  mixed  in  freezing  weather,  the  sand 
and  gravel  or  water  shall  be  heated  sufficiently  before  mixing  to 
remove  all  frost. 

14.  Placing  Concrete. — No  concrete  shall  be  used  that  has 
attained  its  initial  set,  and  such  concrete  shall  be  immediately 
removed  from  the  site  of  the  work.    No  concrete  shall  be  placed 
except  in  the  presence  of  a  duly  authorized  inspector. 

15.  Hauling  Pipe. — In  handling  and  hauling  the  sections  of 
pipe  great  care  shall  be  taken  to  avoid  injury  to  the  pipe,  and 
suitable  cradles  shall  be  provided  to  avoid  concentration  of  the 
entire  weight  on  small  areas.    The  sections  of  pipe  shall  be  dis- 
tributed along  the  trench  as  directed  by  the  engineer.    Any  pipes 
that  are  seriously  injured  in  handling  or  hauling  will  be  re- 
jected and  shall  be  immediately  removed  from  the  site  of  the 
work  or  demolished,  and  the  contractor  shall  replace  the  same 
with  other  sections  of  pipe  having  the  same  quantity  of  rein- 
forcement. 

1 6.  Laying  Pipe. — The  sections  of  pipe  shall  be  laid  true  to 
line  and  grade  according  to  stakes  established  by  the  engineer 
and  with  only  sufficient  joint  space  between  to  allow  for  satis- 
factory caulking.    Before  making  the  joints  the  adjacent  sections 
of  pipe  shall  be  firmly  bedded  or  supported  by  blocks  to  pre- 
vent the  slightest  movement  while  the  joint  is  being  made. 

17.  Joints. — Joints  may  be  made  by  sectional  collars  sepa- 
rately moulded  and  set  in  grooves  in  the  ends  of  the  pipe  sections, 
or  by  pouring  concrete  on  the  outside  of  the  pipe  into  suitable 


352  WORKING  DATA  FOR   IRRIGATION  ENGINEERS 

flexible  forms  and  at  the  same  time  pointing  and  smoothing  off 
on  the  inside  with  a  1  to  1  mixture  of  mortar.  The  concrete 
used  for  joints  shall  be  equal  to  or  better  in  quality  than  that 
used  for  the  pipe.  Each  joint  shall  be  reinforced  with  ....  steel 
rods,  or  the  equivalent  in  area  of  some  other  form  of  reinforce- 
ment satisfactory  to  the  engineer.  As  soon  as  the  joint  has  been 
made  it  shall  be  covered  with  wet  cloths  and  kept  so  covered  for 
ten  days  thereafter.  If  desired,  after  the  concrete  has  attained 
its  final  set,  damp  earth  may  be  substituted  for  the  wet  cloths. 

18.  Tests  of  Pipe. — On  completion  of  the  work,  or  as  soon  as 
possible   thereafter,  the  contractor  shall   make  a  full-pressure 
test  of  the  pipe.    All  leaks  found  at  the  time  of  the  test  shall 
be  made  tight  by  the  contractor.    The  cost  of  making  the  test 
shall  be  borne  by  the  contractor. 

19.  Measurement. — The  price  bid  per  linear  foot  shall  be 
for  pipe  complete  in  place,  ready  for  service,  and  shall  include  all 
material,  except  cement,  entering  into   or   used   on   the  work, 
manufacture,  hauling,  laying,  jointing,  testing,  repairing  leaks, 
etc.,  until  final  inspection  and  acceptance  by  the  engineer.    The 
number  of  linear  feet  of  pipe  in  place  will  be  measured  along  the 
axis  of  the  pipe  after  completion. 

20.  Payments. — 

SPECIFICATIONS  FOR  CAST-IRON  PIPE 

(Based  on  "Standard  Specifications  for  Cast-Iron  Water-Pipe  " 
of  the  American  Water  Works  Association,  adopted  May  12, 
1908.) 

1.  Description. — The  pipes  shall  be  made  with  hub   and 
spigot  joints  and  shall  conform  accurately  to  the  dimensions 
and  weights  and  shall  be  subjected  to  the  tests  required  for 
class   ....   pipe  in  the  "  Standard  Specifications  for  Cast-Iron 
Water  Pipe  "  of  the  American  Water  Works  Association,  adopted 
May  12,  1908.    They  shall  be  straight  and  shall  be  true  circles 
in  section,  with  their  inner  and  outer  surfaces  concentric.    They 
shall  be  at  least  12  feet  in  length,  exclusive  of  socket.     In  all 
respects  not  specifically  mentioned  herein,  the  pipes  and  their 
material  shall  conform  to  the  above-mentioned  specifications. 

2.  Quality  of  Iron. — All  pipes  shall  be  made  of  cast  iron  of 


SPECIFICATIONS  353 

good  quality,  and  of  such  character  as  shall  make  the  metal  of 
castings  strong,  tough,  and  of  even  grain,  and  soft  enough  to 
admit  satisfactorily  of  drilling  and  cutting.  The  metal  shall  be 
made  without  any  admixture  of  cinder  iron  or  other  inferior 
metal,  and  shall  be  remelted  in  a  cupola  or  air  furnace.  Speci- 
men bars  2  inches  wide  and  1  inch  thick  loaded  at  the  middle  of 
a  24-inch  span  shall  carry  a  load  of  not  less  than  2,000  pounds 
and  shall  show  a  deflection  of  not  less  than  0.3  inch  before  break- 
ing, or,  if  preferred,  tensile  tests  may  be  made  which  shall  show 
a  breaking  load  of  not  less  than  20,000  pounds  per  square  inch. 

3.  Test  Pieces. — (This  paragraph  should  state  who  is  to  fur- 
nish test  pieces  and  how  many,  and  what  disposition  is  to  be 
made  of  broken  test  specimens.) 

4.  Quality  of  Castings. — The  pipes  shall  be  smooth,  free 
from  scales,  lumps,  blisters,  blow-holes,  sand-holes,  and  defects 
of  every  nature  that  unfit  them  for  the  use  for  which  they  are 
intended.    No  plugging  or  filling  will  be  allowed. 

5.  Casting  of  Pipe. — The  straight  pipes  shall  be  cast  in  dry 
sand  moulds  in  a  vertical  position.     Pipes  16  inches  or  less  in 
diameter  shall  be  cast  with  the  hub  end  up  or  down  as  specified  in 
the  proposals.    Pipes  18  inches  or  more  in  diameter  shall  be  cast 
with  the  hub  end  down.     The  pipes  shall  not  be  stripped  or 
taken  from  the  pit  while  showing  color  of  heat,  but  shall  be  left 
in  the  flasks  for  a  sufficient  length  of  time  to  prevent  unequal 
contraction  by  subsequent  exposure. 

6.  Diameters. — The  diameters  of  the  sockets  and  the  outside 
diameters  of  the  spigot  ends  of  the  pipes  shall  not  vary  from  the 
standard  dimensions  by  more  than  .06  of  an  inch  for  pipes 
16  inches  or  less  in  diameter;  .08  of  an  inch  fpr  18-inch,  20-inch 
and  24-inch  pipes;  .10  of  an  inch  for  30-inch,  36-inch,  and  42-inch 
pipes;  .12  of  an  inch  for  48-inch,  and  .15  of  an  inch  for  54-inch 
and  60-inch  pipes.     Especial  care  shall  be  taken  to  have  the 
sockets  of  the  required  size.     The  sockets  and  spigots  will  be 
tested  by  circular  gages  and  no  pipe  will  be   received   that   is 
defective  in  joint  from  any  cause. 

7.  Thickness. — For  pipes  whose  standard  thickness  is  less 
than  1  inch,  the  thickness  of  metal  in  the  body  of  the  pipe  shall 
not  be  more  than  .08  of  an  inch  less  than  the  standard  thickness 


354  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

and  for  pipes  whose  standard  thickness  is  1  inch  or  more,  the 
variation  shall  not  exceed  .10  of  an  inch,  except  that  for  spaces 
not  exceeding  8  inches  in  length  in  any  direction,  variations  from 
the  standard  thickness  of  .02  of  an  inch  in  excess  of  the  allow- 
ance above  given  shall  be  permitted. 

8.  Weights. — No  pipe  shall  be  accepted  whose  weight  is 
more  than  5  per  cent  less  than  the  standard  weight  for  pipes 
16  inches  or  less  in  diameter,  and  4  per  cent  less  than  the  stand- 
ard weight  for  pipes  more  than  16  inches  in  diameter,  and  no 
excess  above  the  standard  weight  or  more  than  the  given  per- 
centage will  be  paid  for.    The  total  weight  to  be  paid  for  shall 
not  exceed  for  each  size  and  class  of  pipe  received  the  sum  of 
the  standard  weights  of  the  same  number  of  pieces  of  the  given 
size  and  class  by  more  than  2  per  cent. 

9.  Coating. — Every  pipe  and  special  casting  shall  be  coated, 
inside  and  out,  with  coal-tar  pitch  varnish,  mixed  with  sufficient 
oil  to  make  a  smooth  coating,  tough  and  tenacious  when  cold 
and  not  brittle  nor  with  any  tendency  to  scale  off.    Before  being 
dipped  the  pipes  shall  be  thoroughly  cleaned  and  shall  be  entirely 
free  from  rust.     Castings  shall  have  a  uniform  temperature  of 
300°  F.  when  they  are  put  in  the  vat  and  the  coating  material 
shall  be  kept  heated  to  the  same   temperature.      Each  casting 
shall  remain  in  the  bath  at  least  five  minutes. 

10.  Marking. — Each  pipe  shall  have  distinctly  cast  upon  it 
the  initials  of  the  maker's  name,  and  the  weight  and  class  letter 
shall  be  conspicuously  painted  in  white  on  the  inside  of  each 
pipe  after  the  coating  has  become  hard. 

11.  Inspection  and  Tests. — All  pipes  shall  be  subjected  to  a 
careful  hammer  inspection.    Tests  of  the  material  will  be  made 

by at  its  own  expense,  or  they  may  be  made  at 

the  plant  by  the  contractor  or  his  employees  acting  under  the 
direction  of  the  engineer  or  his  representative;  or  certified  tests 
may,  at  the  option  of  the  engineer,  be  accepted  in  lieu  of  the 
above-mentioned  tests. 

12.  Shipment. — 

13.  Payment. — 


SPECIFICATIONS  355 

SPECIFICATIONS    FOR    METAL    FLUMES 

1.  Type  of  Flume. — All  flumes  furnished  under  these  speci- 
fications shall  be  made  of  metal  and  shall  be  of  the  semicircular, 
smooth-interior  type.    Bidders  shall  submit  with  their  proposals 
a  drawing  or  catalogue  showing  clearly  the  type  of  construction 
and  detailed  dimensions  of  the  flume  that  they  propose  to  fur- 
nish.    Smoothness  of  interior  surface  and  ease  of  erection  will 
be  important  factors  in  the  consideration  of  proposals. 

2.  Dimensions  and  Weight  of  Flume. — The  assembled  flume 
shall  have  an  interior  diameter  of  ....  feet  ....  inches,  and  the 
depth  shall  be  that  of  the  full  semicircle.      The  bidder  shall 
state  the  weight  of  the  completed  flume  per  linear  foot.    A  com- 
plete flume  shall  consist  of  sheets,  carrier  rods,  compression 
bars,  shoes,  nuts,  and  washers. 

3.  Thickness  of  Metal  Sheets. — The  thickness  of  the  metal 
sheets  shall  be  sufficient  to  provide  necessary  rigidity  and  stiff- 
ness.   The  following  minimum  thicknesses  shall  be  used: 

No.  of  Flume  U.  S.  Standard  Gage 

24  to    60 22 

72  to  108 v 20 

120  to  156 18 

168  to  204 16 

216  and  larger 14 

For  the  larger  sizes  of  flumes  intermediate  carrier  rods  or  reinforc- 
ing ribs  shall  be  furnished,  if  necessary,  to  maintain  the  true 
semicircular  shape  of  the  sheets  when  subjected  to  the  full 
weight  of  water  and  the  bidder  shall  submit  a  drawing  or  de- 
scription of  the  method  of  reinforcing  he  proposes  to  use. 

4.  Size  of  Carrier  Rods  and  Compression  Bars. — Carrier 
rods  shall  be  designed  for  a  working  stress  of  8,000  pounds  per 
square  inch  when  subjected  to  the  full  weight  of  the  water; 
provided  that  the  smallest  allowable  carrier  rod  shall  be  %-inch 
in  diameter,  or  its  equivalent.     Carrier  rods  shall  be  threaded 
at  both  ends  and  provided  with  nuts  and  washers.    They  shall 
be  as  strong  in  thread  as  in  body.    Compression  bars  shall  be 
equivalent  to  or  larger  in  cross-section  than  the  corresponding 
carrier  rods.    Compression  bars  shall  be  provided  with  shoes  for 


356 


WORKING  DATA  FOR  IRRIGATION  ENGINEERS 


distributing  the  pressures  on  supporting  timbers.  The  size  and 
shape  of  shoes  and  washers  shall  be  such  as  to  distribute  prop- 
erly the  pressures  on  the  wooden  timbers  supporting  the  flume, 
and  the  average  pressure  on  the  timbers  due  to  the  full  weight 
of  the  water  in  the  flume  shall  not  exceed  400  pounds  per  square 
inch.  All  carrier  rods,  compression  bars,  shoes,  nuts,  and 
washers  shall  be  coated  before  shipment  by  being  dipped  when 
hot  in  a  mixture  of  pure  California  asphalt,  or  its  equivalent; 
not  less  than  7  per  cent  nor  more  than  10  per  cent  of  pure  lin- 
seed oil  shall  be  mixed  with  the  asphalt.  Materials  for  coating 
shall  be  subject  to  the  approval  of  the  engineer. 

5.  Joints. — The  joints  between  successive  sheets  comprising 
the  flume  lining  shall  be  designed  to  be  rigid  and  water  tight 
and  shall  offer  the  least  possible  obstruction  to  the  flow  of  water 
through  the  flume.     All  necessary  crimping  of  sheets  to  form 
the  joints  shall  be  done  by  the  contractor. 

6.  Curves. — The  metal  sheets  for  curved  flumes  shall  be 
fabricated  so  as  to  conform  exactly  to  the  degree  of  curvature 
required.     The  engineer  will  furnish  the  contractor  a  list  of 
lengths  of  flumes  required  of  each  degree  of  curvature,  and  the 
degree  of  curvature  shall  be  plainly  stamped  on  each  sheet. 

7.  Materials  for  Sheets. — The  metal  sheets  shall  be  manu- 
factured  from   steel   or  pure   iron,    and   shall   be   galvanized. 
The  chemical  and  physical  properties  of  the   allowable    mate- 
rials shall  be  as  follows: 


Elements  Considered 

Pure  Iron 

Open-hearth  Steel 

Bessemer  Steel 

Carbon  max.  per  cent  

.03 

0.07  to  0.14 

0.07  to  0.14 

Manganese        "     "    

.03 

0.34  to  0.46 

1.00 

Phosphorus       "     "    

.01 

.03 

.10 

Sulphur             "      "    

.03 

.05 

.07 

Silicon                        '    

.01 

.02 

.02 

Copper               "      "    

Recorded 

Recorded 

Recorded 

Ultimate  strength  

42,000-48,000 

50,000-60,000 

50,000-60,000 

Elastic  limit  

22,000-30,000 

25,000-35,000 

25,000-35,000 

Minimum  elongation  in  8" 

25  per  cent 

25  per  cent 

25  per  cent 

The  material  shall  show  great  homogeneity  of  structure  as 
exhibited  by  the  ends  of  the  broken  test  specimens. 


SPECIFICATIONS  357 

8.  Material  for  Compression  Bars    and    Carrier    Rods. — 

These  shall  be  made  of  medium  steel  and  shall  have  an  ultimate 
tensile  strength  of  55,000  to  65,000  pounds  per  square  inch;  an 
elastic  limit  of  not  less  than  one-half  of  the  ultimate  tensile 
strength;  a  minimum  per  cent  of  elongation  in  8  inches  of 
1,400,000  divided  by  the  ultimate  strength;  a  silky  fracture;  and 
capability  of  being  bent  cold  without  fracture  180°  around  a 
pin  having  a  diameter  equal  to  the  thickness  of  the  test 
piece. 

9.  Material  for  Shoes  and  Washers. — The  bearing  shoes  and 
washers  for  compression  bands  and  carrier  rods  may  be  made 
of  either  gray  or  malleable  cast  iron.     Gray  iron  castings  shall 
conform  in  all  respects  to  the  standard  specifications  for  such 
castings  adopted  September  1,  1905,  by  the  American  Society 
for  Testing  Materials,  except  that  no  tensile  test  will  be  required. 
Malleable  iron  castings  shall  conform  to  the  standard  specifica- 
tions for  such  castings  adopted  November  15,   1904,  by  the 
American  Society  for  Testing  Materials. 

10.  Test  Pieces. — All  test  pieces  shall  be  furnished  by  the 
contractor  at  his  expense.    The  number  and  shape  of  test  speci- 
mens for  gray  and  malleable  castings  shall  be  as  prescribed  in 
the  specifications  of  the  American  Society  for  Testing  Materials 
specified   in   paragraph   9   hereof.     For  all  other  materials,  at 
least  one  test  specimen  shall  be  taken  from  each  melt,  and  where 
possible  shall  be  cut  from  the  finished  material.    Specimens  not 
cut  from  finished  material  shall,  in  so  far  as   possible,    receive 
the  same  treatment  before  testing  as  the  finished  product.    Ten- 
sile test  pieces  shall  be  %  of  an  inch  in  diameter  and  shall  have 
8  inches  of  gage  length. 

11.  Inspection  and  Tests. — All  necessary  facilities  and  as- 
sistance for  making  inspection  and  tests  shall  be  furnished  to 
the  engineer  by  the  contractor  at  the  expense  of  the  contractor. 

Physical  tests  and  chemicals  analyses  will  be  made  by 

at  its  own  expense;  or  they  may  be  made  at  the  factory  by  the 
contractor  or  his  employees,  acting  under  the  direction  of  the 
engineer  or  his  representative;  or  certified  tests  may,  at  the 
option  of  the  engineer,  be  accepted  in  lieu  of  the  above-mentioned 
tests.     No  material  shall  be  shipped  until  all  tests  and  final 


358  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

inspection  have  been  made,  or  certified  tests  shall  have  been 
accepted. 

12.  Galvanizing. — The  metal  sheets  shall  have  a  coating  of 
tight  galvanizing.    The  grooving  for  joints  and  bending  of  sheets 
shall  be  done  in  such  a  manner  as  to  avoid  any  injury^  to  galvan- 
izing.   All  sheets  on  which  the  galvanizing  is  cracked  or  otherwise 
injured  will  be  rejected.    The  galvanizing  shall  consist  of  a  coat- 
ing of  pure  zinc  evenly  and  uniformly  applied  in  such  a  manner 
that  it  will  adhere  firmly  to  the  surface  of  the  metal.     Each 
square  foot  of  metal  sheets  shall  hold  not  less  than  1J/2  ounces  of 
zinc.    The  galvanizing  shall  be  of  such  quality  that  clean,  dry 
samples  of  the  galvanized  metal  shall  appear^  black  and  show 
no  copper-colored  spots  when  they  are  four  times  alternately 
immersed  for  one  minute  in  the  standard  copper  sulphate  solu- 
tion and  then  immediately  washed  in  water  and  thoroughly 
dried.    The  coating  shall  fully  and  completely  cover  all  surfaces 
of  the  material,  and  shall  appear  smooth  and  polished  and  be 
free  from  lumps  of  zinc. 

13.  Shipment. — 

14.  Measurement  and  Payment. — Payment  will  be  made  on 
the  basis  of  the  actual  assembled  length  of  flume  measured  along 
the  center  line  and  at  the  prices  bid  in  the  schedule. 


SPECIFICATIONS  FOR  STEEL  HIGHWAY  BRIDGES 

1.  Description.— The  bridge  shall  be  of  the  {    .   nveted       1 

( pin-connected  J 

I  ,         ,[  truss  type,  having  a  span,  center   to  center  of  end 

bearings,  of  ....  feet  ....  inches,  and  a  clear  width  between 
trusses  of feet.    The  bridge  shall  consist  of spans. 

2.  Stress  Sheets  and  Loading. — The  bidder  shall  furnish  with 
his  bid  a  stress  sheet  showing  the  maximum  stresses  to  which 
members  are  to  be  subjected,  based  on  the  following  loading: 

/  =  span  in  feet. 
w  =  weight  of  steel  per  square  foot  of  floor. 


SPECIFICATIONS  359 

p  =  live  load  per  square  foot  of  floor. 

Dead  load :  w  =  not  less  than  the  actual  weight  of  steel. 
Wooden  floor  =15  pounds  per  square  foot. 

Live  load:  p  =  100  —  io  or  a  concentrated  load  of 
30,000  pounds  on  two  axles  8  feet  center  to 
center;  with  wheels  spaced  6  feet  center  to 
center,  and  two-thirds  of  the  load  on  one 
axle,  assumed  to  occupy  a  space  16  feet  in 
the  direction  of  traffic  by  12  feet  at  right 
angles  thereto. 

Impact:  for  chords  25  per  cent  of  uniform  live  load; 

for  web  and  floor,  40  per  cent  of  either  uni- 
form or  concentrated  live  load. 

Wind  load:  unloaded  chord,  100  pounds  per  linear  foot 
of  bridge. 

loaded  chord,  200  pounds  per  linear  foot 
of  bridge. 

Note. — Neither  wind  nor  concentrated  loads  are  assumed  to 
act  simultaneously  with  uniform  live  load. 

3.  Detail  Drawings. — The  contractor  shall  prepare  all  detail 
and  shop  drawings.  Each  proposal  shall  be  accompanied,  in 
addition  to  the  stress  sheets,  by  such  general  drawings  of  members 
and  details  as  will  clearly  show  the  type  of  construction  proposed 
at  all  points,  and  all  items  that  are  necessary  to  enable  the 
engineer  to  determine  the  strength  of  all  parts  of  the  structure 
and  whether,  as  a  whole  and  in  all  its  parts,  it  complies  with 
these  specifications.  As  soon  as  practicable  after  the  award  of 
the  contract  complete  detail  and  shop  drawings  shall  be  furnished 
to  the  engineer  by  the  contractor,  and  these  shall  receive  the 
approval  of  the  engineer  before  work  is  commenced.  Working 
drawings  shall  be  furnished  in  triplicate.  The  approval  of  gen- 
eral and  working  drawings  shall  not  relieve  the  contractor  from 
the  responsibility  of  any  errors  therein.  In  case  the  engineer 
requires  additional  copies  of  drawings  for  use  during  construc- 
tion or  for  record  these  shall  be  furnished  by  the  contractor  with- 
out charge. 


360  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

4.  Unit  Stresses. — The  following  limiting  working  stresses 
in  pounds  per  square  inch  of  net  cross-section  shall  be  used: 

Tension  on  rolled  sections 16,000 

Shear  on  rolled  sections 9,000 

Bearing  on  pins 20,000 

Shear  on  pins 10,000 

Bearing  on  shop  rivets 20,000 

Shear  on  shop  rivets 10,000 

Bearing  on  field  rivets 15,000 

Shear  on  field  rivets 7,500          L 

Bearing  on  columns 16,000 — 70  — 

Bearing  on  expansion  rollers  per  linear  inch 500  d 


d  =  diameter  of  roller  in  inches. 

L  =  unsupported  length  of  column  in  inches. 

R  =  least  radius  of  gyration  in  inches. 

No  compression  member  shall  have  an  unsupported  length 
exceeding  120  times  its  least  radius  of  gyration  for  main  mem- 
bers, or  140  times  its  least  radius  of  gyration  for  laterals. 

5.  Reversed   Stresses. — Members   subject   to   reversion   of 
stresses  shall  be  designed  to  resist  both  tension  and  compression 
and  each  stress  shall  be  increased  by  /(o  of  the  smaller  stress  for 
determining  the  sectional  area.     The  connections  shall  be  de- 
signed for  the  arithmetical  sum  of  the  stresses. 

6.  Combined   Stresses. — Members   subject   to   both   direct 
and  bending  stresses  shall  be  designed  so  that  the  greatest  unit 
fiber  stress  shall  not  exceed  the  allowable  unit  stress  for  the 
member. 

7.  Net  Sections. — The  net  section  of  any  tension  flange  or 
member  shall  be  determined  by  a  plane  cutting  the  member 
square  across  at  any  point.    The  greatest  number  of  rivet  holes 
that  can  be  cut  by  any  such  plane,  or  whose  centers  come  nearer 
than  2 1/2  inches  to  said  plane,  are  to  be  deducted  from  the 
cross-section  when  computing  the  net  area. 

8.  Minimum  Sizes. — No  metal  less  than  /ie  inch  in  thick- 
ness shall  be  used  except  for  filling  plates.    The  smallest  angles 
used  shall  not  be  less  than  2}/£  X  2j^  X  %e  inches.     A  single 
angle  shall  never  be  used  for  a  compression  member. 

9.  Connections. — All  connections  shall  be  designed  to  de- 


SPECIFICATIONS  361 

velop  the  full  strength  of  the  members.  Connecting  plates  shall 
be  used  for  connecting  all  members,  and  in  no  case  shall  any  two 
members  be  connected  directly  by  their  flanges.  Angles  subject 
to  tensile  stress  shall  be  connected  by  both  legs,  otherwise  only 
the  section  of  the  leg  actually  connected  will  be  considered 
effective. 

10.  Portal  Bracing. — Portal  bracing  shall  consist  of  straight 
members  and  shall  be  designed  to  transmit  the  full  wind  reaction 
from  the  upper  lateral  system  into  the  end  posts  and  abutments. 
The  clear  head  room  below  portal  and  sway  bracing  for  a  width 
of  6  feet  on  either  side  of  center  line  shall  be  not  less  than  15 
feet. 

11.  Sway  Bracing. — Sway  bracing  of  an  approved  type  shall 
be  provided  at  each  panel  point. 

12.  Lateral    Systems. — Upper    and    lower    lateral    systems 
shall  be  designed  to  resist  the  maximum  wind  pressures  from 
either  direction.    The  members  shall  be  as  nearly  as  practicable  in 
the  plane  of  the  axes  of  the  chords. 

13.  Floor  System. — All  floor  beams  and  stringers  shall  be 
rolled  or  riveted  steel  girders.     Floor  beams  shall  be  rigidly 
connected  to  the  trusses  and  stringers  shall  be  rigidly  connected 
to  the  floor  beams. 

14.  Intersection  of  Axes  of  Members. — The  axes  of  all  mem- 
bers of  trusses,  and  those  of  lateral  systems  coming  together  at 
any  apex  of  a  truss  or  girder  must  intersect  at  a  point  whenever 
such  an  arrangement  is  practicable,  otherwise  all  induced  stresses 
and  bend  of  members  caused  by  the  eccentricity  must  be. pro- 
vided for. 

15.  Batten  Plates  and  Lattice  Bars. — The  open  sides  of  com- 
pression members  shall  be  stayed  by  batten  plates  at  the  ends 
and  by  diagonal  lattice  bars  at  intermediate  points.     Batten 
plates  shall  be  used  at  intermediate  points  when,  for  any  reason, 
the  latticing  is  interrupted.    Lattice  bars  shall  be  inclined  to  the 
member  not  less   than  60°  for  single  latticing  nor  less  than 
45°  for  double  latticing. 

1 6.  Eyebars. — The  thickness  of  eyebars  shall  be  not  less  than 
%  inch  nor  less  than  l/7  the  width  of  the  bar.    Heads  of  eyebars 
shall  be  formed  by  upsetting  and  forging  and  shall  be  so  proper- 


362  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

tioned  as  to  develop  the  full  strength  of  the  bar.  Eyebars  shall 
be  perfectly  straight  at  the  time  they  are  bored,  and  all  bars 
composing  one  member  shall  be  piled,  clamped  together,  and 
bored  in  one  operation.  The  eyebars  composing  a  member  shall 
be  so  arranged  that  their  surfaces  are  not  in  contact. 

17.  Rods. — No  rod  shall  be  used  which  has  a  cross-sectional 
area  less  than  %  square  inch.    Screw-ends  shall  be  stronger  in 
thread  than  in  body. 

1 8.  Riveting. — The  rivets  used  shall  in  general  be  %  inch  in 
diameter;  smaller  ones  being  allowable  where  made  necessary 
by  the  size  of  the  member,  but  no  rivets  smaller  than  %  inch 
in  diameter  shall  be  used  in  legs  of  an  angle  iron  equal  to  or 
greater  than  3^  inches  wide.    Not  less  than  three  rivets  shall 
be  used  in  any  main  truss,  portal,  or  lower  lateral  connection  or 
in  any  compression  strut  or  sway  bracing,  portal  bracing,  or 
upper  lateral  system  connection.    The  pitch  of  rivets  in  all  classes 
of  work  in  the  direction  of  the  stress  shall  never  exceed  6  inches 
nor  be  less  than  three  diameters  of  the  rivet.    At  the  ends  of 
compression  members  it  shall  not  exceed  four  times  the  diameter 
of  the  rivets  for  a  length  equal  to  twice  the  width  of  the  member. 
No  rivet-hole  center  shall  be  less  than  one  and  one-half  diameters 
from  the  edge  of  the  plate,  and  whenever  practicable  this  distance 
is  to  be  increased  to  two  diameters.    The  rivets  when  driven  must 
completely  fill  the  holes.    The  rivet  heads  must  be  round,  and 
they  must  be  of  uniform  size  for  the  same  size  rivets  throughout 
the  work;  they  must  be  neatly  made  and  concentric  with  the 
rivets  and  must  thoroughly  pinch  the  connected  pieces  together. 
Whenever  possible,  all  rivets  shall  be  machine  driven.    No  rivet 
excepting  those  in  shoe  plates  and  roller  and  bed  plates  is  to 
have  a  smaller  diameter  than  the  thickness  of  the  thickest  plate 
through  which  it  passes.     The  effective  diameter  of  any  rivet 
shall  be  assumed  the  same  as  its  diameter  before  driving,  but  in 
making   deductions   for   rivet   holes   in   tension   members   the 
diameter  of  the  hole  shall  be  assumed  %  inch  larger  than  that  of 
the  rivet.     The  amount  of  field  riveting  shall  be  reduced  to  a 
minimum,  and  all  details  are  to  be  made  so  that  the  field  rivets 
can  be  driven  readily.     Rivets  shall  not  be  used  in  direct  ten- 
sion.    The  contractor  will  be  held  responsible  for  the  correct 


SPECIFICATIONS  363 

fitting  of  all  parts  upon  assembly  in  the  field,  and,  if  necessary 
to  insure  this,  all  members  shall  be  assembled  in  the  shop,  and 
fitted  before  shipment. 

19.  Pins. — All  pins  shall  be  turned  smoothly  to  a  gage  and 
shall  be  finished  perfectly  round,  smooth,  and  straight.    All  pins 
up  to  and  including  3j/£  inches  in  diameter  shall  fit  the  pin-holes 
within  1/50  inch;  all  pins  over  3^2  inches  in  diameter  shall  fit 
their  holes  within  1/32  inch.     The  contractor  must  provide 
steel-pilot  nuts  for  all  pins  to  preserve  the  threads  while  the 
pins  are  being  driven. 

20.  Camber. — All  trusses  shall  be  cambered  by  making  the 
top-chord  section  longer  than  the  corresponding  bottom-chord 
section  by  /{6  inch  for  each  10  feet  of  length. 

21.  Expansion  and  Contraction. — Provision  shall  be  made 
for  changes  in  length  due  to  temperature  variations  of  at  least 
y*  inch  for  each  10  feet  of  span. 

22.  Roller  Ends. — Each  truss  of  more  than  60  feet  span 
shall  be  provided  with  one  roller  end.    For  spans  60  feet  and 
less  a  sliding  end  may  be  used.    Rollers  shall  be  turned  accurately 
to  gage  and  must  be  finished  perfectly  round  and  to  the  correct 
diameter  or  diameters  from  end  to  end.     The  tongues  and 
grooves  in  plates  and  rollers  must  fit  snugly  so  as  to  prevent 
lateral  motion.     Roller  beds  must  be  planed.     The  smallest 
allowable  diameter  of  expansion  rollers  is  3^2  inches. 

23.  Anchorages. — Every  span  must  be  anchored  at  each 
end  to  the  pier  or  abutment  in  such  a  manner  as  to  prevent 
lateral  motion,  but  so  as  not  to  interfere  with  the  longitudinal 
motion  of  the  truss  due  to  changes  of  temperature.    The  shoes 
or  bolsters  shall  be  so  located  that  the  anchor  bolts  will  occupy 
a  central  position  in  the  slotted  holes  at  a  temperature  of  40° 
F.     Bedplates  shall  be  designed  to  distribute    the  load  over 
a  sufficient  area  to  keep  the  pressure  on  the  masonry  below  400 
pounds  per  square  inch. 

24.  Hand  Railing. — A  suitable  latticed  hand  railing  shall  be 
provided  for  each  truss. 

25.  Shop  Painting. — Before  leaving   the  shop  all  structural 
steel,  except  as  below  specified,  shall  be  thoroughly  cleaned  of 
all  loose  scales  and  rust  and  given  one  coat  of  good  iron  ore  paint 


364  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

mixed  with  pure  linseed  oil,  which  shall  be  well  worked  into  all 
joints  and  open  spaces.  All  surfaces  of  steel  that  will  come  in 
contact  with  each  other  shall  be  painted  before  being  riveted  or 
bolted  together.  Pins,  pinholes,  screw  threads,  and  all  finished 
surfaces  shall  not  be  painted,  but  shall  be  coated  with  white 
lead  and  tallow  as  soon  as  they  are  finished. 

MATERIAL 

26.  Manufacture. — Structural  steel  shall  be  made  by  the 
open-hearth  process  and  shall  conform  in  all  respects,  not  spe- 
cifically mentioned  herein,  to  the  "  Standard  Specifications  for 
Structural  Steel  for  Bridges  of  the  American  Society  for  Testing 
Materials,"  adopted  August  25,  1913. 

27.  Physical  and  Chemical  Properties  of  Structural  Steel. — 
Steel  shall  contain  not  more  than  0.05  per  cent  sulphur,  and  not 
more  than  0.04  per  cent  phosphorus  for  basic  open-hearth  nor 
more  than  0.06  per  cent  phosphorus  for  acid  open-hearth.     It 
shall  have  an  ultimate  tensile  strength  of  55,000  to  65,000  pounds 
per  square  inch;  an  elastic  limit  as  indicated  by  the  drop  of  beam 
of  not  less  than  one-half  the  ultimate  tensile  strength;  a  mini- 
mum per  cent  of  elongation  in  8  inches  of  1,500,000  divided  by 
the  ultimate  tensile  strength;   a  silky  fracture  and  capability 
of   being   bent   cold  without    fracture    180°  flat  on  itself  for 
material  %  inch  thick  and  under;  for  material  over  %  inch  to 
and  including  1  %  inches  around  a  pin  having  a  diameter  equal  to 
the  thickness  of  the  test  piece;  and  for  material  over  lj^  inches 
thick,  around  a  pin  having  a  diameter  equal  to  twice  the  thick- 
ness of  the  test  piece.    A  deduction  of  2.5  will  be  allowed  in  the 
specified  percentage  of  elongation  for  each  /(6  inch  in  thickness 
below  /{6  inch  and  a  deduction  of  1  will  be  allowed  for  each  H  inch 
in  thickness  above  %  inch. 

28.  Physical  and  Chemical  Properties  of  Rivet  Steel. — Rivet 
steel  shall  contain  not  more  than  .04  per  cent  each  of  sulphur 
and  phosphorus.    It  shall  have  an  ultimate  tensile  strength  of 
45,000  to  55,000  pounds  per  square  inch;  an  elastic  limit  as 
determined  by  the  drop  of  beam  of  not  less  than  one-half  the 
ultimate  tensile  strength;  a  minimum  per  cent  of  elongation  in 
8  inches  of  1,500,000  divided  by  the  ultimate  tensile  strength; 


SPECIFICATIONS  365 

a  silky  fracture;  and  capability  of  being  bent  cold  without 
fracture  180°  flat  on  itself. 

29.  Finish. — Finished  material  must  be  free  from  injurious 
seams,  flaws,  or  cracks,  and  have  a  workmanlike  finish. 

30.  Marking. — Every  finished  piece  of  steel  shall  have  the 
melt  number  stamped  or  rolled  upon  it.    Steel  for  pins  and  rollers 
shall  be  stamped  on  the  end.    Rivet  steel  and  other  small  parts 
may  be  bundled,  with  the  above  marks  on  an  attached  metal 
tag. 

31.  Test  Pieces.      (This  paragraph  should  state  who  is  to 
furnish  test  pieces  and  how  many,  and  what  disposition  is  to  be 
made  of  the  broken  test  specimens,  etc.) 

32.  Tests.      (This  paragraph  should  state  who  is  to  make 
tests,  at  whose  expense  tests  are  to  be  made,  etc.) 

33.  Shipment. 

34.  Payment  for  Fabricated  Material. — 

t  i 

ERECTION 

35.  Material  and  Labor. — The  contractor  shall  furnish  all 
labor,  tools,  machinery,  and  materials,  except  wood  flooring,  for 
erecting  the  bridge  complete  in  place,  including  all  hauling, 
erection,  and  dismantling  of  all  falsework  and  staging,  setting 
of  anchor  bolts,  and  all  other  work  necessary  for  the  completion 
of  the  structure  ready  for  traffic. 

36.  Wood  Floor. — Lumber  for  flooring  shall  be   furnished, 
and  put  in  place  by  the  contractor  and  he  shall  furnish  all 
necessary  fastenings.      Flooring   shall   be  4  inches  thick  and 
shall  be  of  sound  timbers  of  good  grade,  rough.     A  4  x  8  inch 
wheel-guard  shall  be  placed  adjacent  to  each  truss. 

37.  Painting  After  Erection. — After  erection  all  metal  work 
shall  be  thoroughly  cleaned  of  mud,  grease,  and  other  objection- 
able matter  and  evenly  painted  with  two  coats  of  paint  of  the 
kind  and  colors  specified  by  the  engineer.    Linseed  oil  shall  be 
used  as  the  vehicle  in  mixing  the  paint  for  each  of  these  coats, 
and  the  separate  coats  shall  have  distinctly  different  shades  of 
color.    All  recesses  which  might  retain  water  shall  be  filled  with 
thick  paint  or  some  water-proof  material  before  final  painting. 
The  first  coat  shall  be  allowed  to  become  thoroughly  dry  before 


366  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

the  second  coat  is  applied.    No  painting  shall  be  done  in  wet  or 
freezing  weather. 

38.  Final  Payment.— 

SPECIFICATIONS  FOR  CONCRETE 

1.  Composition. — Concrete  shall  be  composed  of  cement, 
sand,  and  broken  rock  or  clean  gravel,  well  mixed  and  brought 
to  a  proper  consistency  by  the  addition  of  water.     Ordinarily 
one  part  by  volume,  measured  loose,  of  cement  shall  be  used 

with parts  of  sand  and parts  of  broken  rock  or 

gravel.    These  proportions  may  be  modified  by  the  engineer  as 
the  work  or  the  nature  of  the  materials  used  may  render  it 
desirable,  and  the  contractor  shall  not  be  entitled  to  any  extra 
compensation  by  reason  of  such  modifications. 

(Note. — //  the  contractor  furnishes  the  cement  this  paragraph 
must  be  modified  to  provide  for  different  prices  for  different  mix- 
tures.) 

2.  Cement.     (See  specifications  for  cement.) 

3.  Reinforcement  Bars. — Steel  bars  shall  be  placed  in  the 
concrete  wherever  shown  in  the  drawings  or  prescribed  by  the 
engineer.    The  exact  position  and  shape  of  reinforcement  bars 
are  not  shown  in  all  cases  in  the  drawings  accompanying  these 
specifications,   but   the   contractor   will   be   furnished   supple- 
mental detailed  drawings  and  lists  which  will  give  him  the  infor- 
mation necessary  for  cutting,  bending,  and  spacing  of  bars.    The 
steel  used  for  concrete  reinforcement  shall  be  so  secured  in 
position  that  it  will  not  be  displaced  during  the  depositing  of 
the  concrete,  and  special  care  shall  be  exercised  to  prevent  any 
disturbance  of  the  steel  in  concrete  that  has  already  been  placed. 

4.  Sand. — Sand  for  concrete  may  be  obtained  from  natural 
deposits  or  may  be  made  by  crushing  suitable  rock.    The  sand 
particles  shall  be  hard,  dense,  durable  rock  fragments,  such  as 
will  pass  a  ^-mch  mesh  screen.    The  sand  must  be  free  from 
organic  matter  and  must  not  contain  more  than  5  per  cent  of 
clayey  and  other  objectionable  non-organic  material.    The  sand 
must  be  so  graded  that  when  dry  and  well  shaken  its  voids  will 
not  exceed  35  per  cent. 

5.  Broken  Rock  or  Gravel. — The  broken  rock  or  gravel  for 


SPECIFICATIONS  367 

concrete  must  be  hard,  dense,  durable  rock  fragments  or  pebbles 

that  will  pass  through  a -inch  mesh  screen  when  used  for 

plain  concrete,  and  through  a -inch  mesh  screen  when  used 

for  reinforced  concrete,  and  that  will  be  rejected  by  a  J^-inch 
mesh  screen. 

6.  Water. — The  water  used  in  mixing  concrete  must  be 
reasonably  clean  and  free  from  objectionable  quantities  of  or- 
ganic matter,  alkali  salts,  and  other  impurities. 

7.  Mixing. — The  cement,  sand,  and  broken  rock  or  gravel 
shall  be  so  mixed  and  the  quantities  of  water  added  shall  be 
such  as  to  produce  a  homogeneous  mass  of  uniform  consistency. 
Dirt  and  other  foreign  substance  shall  be  carefully  excluded. 
Machine  mixing  will  be  required  unless  specific  authority  to 
use  hand  mixing  is  given  by  the  engineer.    The  machine  and 
its  operation  shall  be  subject  to  the  approval  of  the  engineer. 
Hand  mixing,   if  permitted,   shall  be  thorough  and  shall  be 
done  on  a  clean,  tight  floor.    In  general,  enough  water  shall  be 
used  in  mixing  to  give  the  concrete  the  consistency  ordinarily 
designated  as  "  wet."    Concrete  containing  a  minimum  amount 
of  water,   ordinarily  designated  as  "  dry "   concrete,  will  be 
permitted  only  where  the  nature  of  the  work  renders  the  use  of 
"  wet  "  concrete  impracticable.    If  concrete  is  mixed  in  freezing 
weather,  the  materials  shall  be  heated  sufficiently  before  mixing 
to  remove  all  frost  and  maintain  a  temperature  above  32°  F., 
until  the  concrete  has  been  placed  in  the  work  and  has  attained 
its  final  set. 

8.  Placing. — Concrete  shall  be  placed  in  the  work  before 
the  cement  takes  its  initial  set.    No  concrete  shall  be  placed  in 
water  except  by  permission  of  the  engineer  and  the  method  of 
depositing  the  same  shall  be  subject  to  his  approval.    Foundation 
surfaces  upon  which  concrete  is  to  be  placed  must  be  free  from 
mud  and  debris.    When  the  placing  of  concrete  is  to  be  inter- 
rupted long  enough  for  the  concrete  to  take  its  final  set,  the 
working  face  shall  be  given  a  shape,  by  the  use  of  forms  or 
other  means,  at  the  option  of  the  engineer,  that  will  secure 
proper   union  with   subsequent  work.     All   concrete  surfaces 
upon  or  against  which  concrete  is  to  be  placed  and  to  which 
the  new  concrete  is  to  adhere,  shall  be  roughened,  thoroughly 


368  WORKING  DATA   FOR   IRRIGATION  ENGINEERS 

cleaned,  and  wet  before  the  concrete  is  deposited.  "  Dry  " 
concrete  shall  be  deposited  in  layers  not  exceeding  6  inches  in 
thickness,  each  of  which  shall  be  rammed  until  water  appears 
on  the  surface.  "  Wet "  concrete  shall  be  stirred  with  suitable 
tamping  bars,  shovels,  or  forked  tools  until  it  completely  fills 
the  form,  closes  snugly  against  all  surfaces,  and  is  in  perfect  and 
complete  contact  with  any  steel  used  for  reinforcement.  Where 
smooth  surfaces  are  required  a  suitable  tool  shall  be  worked  up 
and  down  next  to  the  form  until  the  coarser  material  is  forced 
back  and  a  mortar  layer  is  brought  next  to  the  form.  No  concrete 
shall  be  placed  except  in  the  presence  of  a  duly  authorized 
inspector. 

9.  Finishing. — The  surface  of  concrete  finished  against  forms 
must  be  smooth,  free  from  projections,  and  thoroughly  filled  with 
mortar.    Immediately  upon  the  removal  of  forms  all  voids  shall 
be  neatly  filled  with  cement  mortar,  irregularities  in  exposed 
surfaces  shall  be  removed  and  minor  imperfections  of  finish 
shall  be  smoothed  to  the  satisfaction  of  the  engineer.    Exposed 
surfaces  of  concrete  not  finished  against  forms,  such  as  horizontal 
or  sloping  surfaces,  shall  be  brought  to  a  uniform  surface  and 
worked  with  suitable  tools  to  a  smooth  mortar  finish.    All  sharp 
angles  where  required  shall  be  rounded  or  bevelled  by  the  use  of 
moulding  strips  or  suitable  moulding  or  finishing  tools. 

10.  Protection. — The  contractor  shall  protect  all   concrete 
against  injury.    Exposed  surfaces  of  concrete  shall  be  protected 
from  the  direct  rays  of  the  sun  and  shall  be  kept  damp  for  at 
least  two  weeks  after  the  concrete  has  been  placed.    Concrete 
laid  in  cold  weather  shall  be  protected  from  freezing  by  such 
means  as  are  approved  by  the  engineer.    All  damage  to  concrete 
shall  be  repaired  by  the  contractor  at  his  expense,  in  a  manner 
satisfactory  to  the  engineer. 

11.  Forms. — Forms  to  confine  the  concrete  and  shape  it  to 
the  required  lines  shall  be  used  wherever  necessary.    Where  the 
character  of  the  material  cut  into  to  receive  a  concrete  structure 
is  such  that  it  can  be  trimmed  to  the  prescribed  lines,  the  use  of 
forms  will  not  be  required.     The  forms  shall  be  of  sufficient 
strength  and  rigidity  to  hold  the  concrete  and  to  withstand  the 
necessary  pressure  and  ramming  without  deflection  from  the 


SPECIFICATIONS  369 

prescribed  lines.  For  concrete  surfaces  that  will  be  exposed  to 
view  and  for  all  other  concrete  surfaces  that  are  to  be  finished 
smooth,  the  lagging  of  forms  must  be  surfaced  and  bevel-edged 
or  matched;  provided  that  smooth  metal  forms  may  be  used  if 
desired.  All  forms  shall  be  removed  by  the  contractor,  but  not 
until  the  engineer  gives  permission.  Forms  may  be  used  repeat- 
edly, provided  they  are  maintained  in  serviceable  condition  and 
thoroughly  cleaned  before  being  re-used. 

12.  Measurement. — Concrete  will  be  measured  for  payment 
to  the  neat  lines  shown  in  the  drawings  or  prescribed  by  the 
engineer  under  these  specifications.    No  payments  will  be  made 
for  concrete  outside  of  the  prescribed  lines. 

13.  Payment. — The  unit  price  bid  for  concrete  shall  include 
all  material  and  labor  entering  into  its  construction. 

SPECIFICATIONS  FOR  PAVING 

1.  Dry  Paving. — Where  shown  in  the  drawings  and  where 
directed  by  the  engineer,  dry  paving  shall  be  placed  on  the 
embankment  slopes  and  on  the  beds  and  banks  of  canals  and 
other  watercourses.    The  rock  used  for  paving  shall  be  clean, 
hard,  dense,   and  durable.     The  dimensions  of  paving  stone 

normal  to  the  face  of  the  pavement  shall  be  not  less  than 

inches.     They  shall  have  an  average  volume  of  not  less  than 

of  a  cubic  foot,  not  more  than  25  per  cent  of  the  pieces  being 

less  than  ....  of  a  cubic  foot  in  volume.     Either  boulders  or 
quarried  rock  may  be  used  if  fulfilling  the  requirements  as  to 
quality  and  dimensions.     If  quarried  rock  is  used,  the  stones 
shall  have  roughly  squared,  reasonably  flat,  upper  faces.    The 
stones  shall  be  bedded  in  a  layer  of  sand  and  gravel  or  unscreened 
crushed  rock,  having  an  average  thickness  of  not  less  than  .... 
inches.    They  shall  be  hand  placed  with  close  joints  to  the  lines 
and  grades  established  by  the  engineer,  and  the  spaces  between 
the  stones  shall  be  filled  with  spalls  and  gravel  or  crushed  rock. 
The  thickness  of  the  paving,  including  the  gravel  layer,  shall  be 
not  less  than  ....  inches.    Payment  for  dry  paving  will  be  made 
at  the  unit  prices  per  square  yard  bid  therefor  in  the  schedules. 

2.  Grouted  Paving. — Where  shown  in  the  drawings  and  where 
directed  by  the  engineer,  grouted  paving  shall  be  placed  on  the 


370  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

embankment  slopes  and  on  the  beds  and  banks  of  canals  and 
other  watercourses.  The  rock  used  for  paving  shall  be  clean, 
hard,  dense,  and  durable.  The  dimension  of  paving  stones  normal 
to  the  face  of  the  pavement  shall  be  not  less  than  ....  inches. 
They  shall  have  an  average  volume  of  not  less  than  ....  of  a 
cubic  foot,  not  more  than  25  per  cent  of  the  pieces  being  less 
than  ....  of  a  cubic  foot  in  volume.  Either  boulders  or  quarried 
rock  may  be  used  if  fulfilling  the  requirements  as  to  quality  and 
dimensions.  If  quarried  rock  is  used,  the  stones  shall  have 
roughly  squared,  reasonably  flat,  upper  faces.  The  stones  shall  be 
bedded  in  a  layer  of  sand  and  gravel  or  unscreened  crushed  rock, 
having  an  average  thickness  of  not  less  than  ....  inches.  They 
shall  be  hand  placed  with  close  joints  to  the  lines  and  grades 
established  by  the  engineer  and  the  spaces  between  the  stones 
shall  be  filled  with  spalls  and  gravel  or  crushed  rock,  from 
which  the  sand  or  fine  material  has  been  removed  by  screening,, 
after  which  a  mortar,  composed  of  three  parts  sand  and  one  part 
cement,  shall  be  poured  into  the  voids  so  as  to  form  a  water-tight 
surface.  After  the  cement  mortar  has  been  added  the  paving 
shall  be  kept  moist  for  forty-eight  hours  after  the  cement  has 
reached  its  permanent  set.  The  thickness  of  paving,  including 

the  gravel  layer,  shall  be  not  less  than inches.    Payment  for 

grouted  paving  will  be  made  at  the  unit  prices  per  square  yard 
bid  therefor  in  the  schedules. 

3.  Rubble  Concrete  Paving. — Where  shown  in  the  drawings 
and  where  directed  by  the  engineer,  rubble  concrete  paving  shall 
be  placed  on  the  embankment  slopes  and  on  the  beds  and  banks 
of  canals  and  other  watercourses.  The  rock  used  for  paving 
shall  be  clean,  hard,  dense,  and  durable.  The  dimension  of 
paving  stones  normal  to  the  face  of  the  paving  shall  be  not  less 
than  ....  inches.  They  shall  have  an  average  volume  of  not 
less  than  ....  of  a  cubic  foot,  not  more  than  25  per  cent  of  the 

pieces  being  less  than of  a  cubic  foot  in  volume.     Either 

boulders  or  quarried  rock  may  be  used  if  fulfilling  the  require- 
ments as  to  quality  and  dimensions.  If  quarried  rock  is  used  the 
stones  shall  have  roughly  squared,  reasonably  flat,  upper  faces. 
The  paving  shall  have  a  foundation  course  of  sand  and  gravel  or 
unscreened  crushed  rock  not  less  than  .  .  inches  in  thickness. 


SPECIFICATIONS  371 

Upon  this  foundation  course  shall  be  placed  a  layer  of  concrete 

inches  thick.    The  paving  stones  shall  be  bedded  in  this 

concrete  before  the  concrete  has  taken  its  initial  set.  The  stones 
shall  be  hand  placed  with  close  joints  to  the  lines  and  grades 
established  by  the  engineer  and  the  spaces  between-  the  stones 
shall  be  filled  with  spalls  or  with  gravel  or  crushed  rock  from 
which  the  sand  or  fine  material  has  been  removed  by  screening, 
after  which  a  mortar  composed  of  three  parts  sand  and  one  part 
cement  shall  be  poured  into  the  voids  so  as  to  form  a  water-tight 
surface.  After  the  cement  mortar  has  been  added,  the  paving 
shall  be  kept  moist  for  forty-eight  hours  after  the  cement  has 
reached  its  permanent  set.  The  thickness  of  paving,  including 
the  gravel  layer  shall  be  not  less  than  ....  inches.  Payment  for 
rubble-concrete  paving  will  be  made  at  the  unit  prices  per  square 
yard  bid  therefor  in  the  schedule. 

SPECIFICATIONS  FOR  CEMENT 

1.  Definition. — The  cement  shall  be  the  product  obtained  by 
finely  pulverized   clinker  produced  by   calcining   to  incipient 
fusion,  an  intimate  mixture  of  properly  proportioned  argillaceous 
and  calcareous  substances,  with  only  such  additions  subsequent 
to  calcining  as  may  be  necessary  to  control  certain  properties. 
Such  additions  shall  not  exceed  3  per  cent,  by  weight,  of  the 
calcined  product. 

2.  Composition. — In  the  finished  cement,  the  following  limits 
shall  not  be  exceeded: 

Per  cent 

Loss  on  ignition  for  15  minutes 4 

Insoluble  residue 1 

Sulphuric  anhydride  (SO3) 1.75 

Magnesia  (MgO) 4 

3.  Specific  Gravity. — The  specific  gravity  of  the  cement  shall 
be  not  less  than  3.10.    Should  the  cement  as  received  fall  below 
this  requirement,  a  second  test  may  be  made  upon  a  sample 
heated  for  thirty  minutes  at  a  very  dull  red  heat. 

4. ,  Fineness. — At  least  92  per  cent  of  the  cement  by  weight 
shall  pass  through  the  No.  100  sieve,  and  at  least  75  per  cent 
shall  pass  through  the  No.  200  sieve. 


372  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

5.  Soundness. — Pats  of  neat  cement  prepared  and  treated 
as  hereinafter  prescribed  shall  remain  firm  and  hard  and  show 
no  sign  of  distortion,  checking,  cracking,  or  disintegration.     If 
the  cement  fails  to  meet  the  prescribed  steaming  test,  the  cement 
may  be  rejected  or  the  steaming  test  repeated  after  seven  or  more 
days,  at  the  option  of  the  engineer. 

6.  Time  of  Setting. — The  cement  shall  not  acquire  its  initial 
set  in  less  than  forty-five  minutes  and  must  have  acquired  its 
final  set  within  ten  hours. 

7.  Tensile  Strength. — Briquettes  made  of  neat  cement,  after 
being  kept  in  moist  air  for  twenty-four  hours  and  the  rest  of  the 
time  in  water,  shall  develop  tensile  strengths  per  square  inch  as 
follows : 

Pounds 

After  seven  days 500 

After  twenty-eight  days 600 

Briquettes  made  up  of  one  part  cement  and  three  parts 
standard  Ottawa  sand,  by  weight,  shall  develop  tensile  strengths 
per  square  inch  as  follows : 

Pounds 

After  seven  days 200 

After  twenty-eight  days 275 

The  average  of  the  tensile  strengths  developed  at  each  age 
by  the  briquettes  in  any  set  made  from  one  sample  is  to  be  con- 
sidered the  strength  of  the  sample  at  that  age,  excluding  any 
results  that  are  manifestly  faulty.  The  average  strength  of  the 
sand  mortar  briquettes  at  twenty-eight  days  shall  show  an 
increase  over  the  average  strength  at  seven  days. 

8.  Brand. — Bids  for  furnishing  cement  or  for  doing  work  in 
which  cement  is  to  be  used  shall  state  the  brand  of  cement  pro- 
posed to  be  furnished  and  the  mill  at  which  made.    The  right  is 
reserved  to  reject  any  cement  which  has  not  established  itself 
as  a  high-grade  Portland  cement,  and  has  not  been  made  by  the 
same  mill  for  two  years  and  given  satisfaction  in  use  for  at  least 
one  year  under  climatic  and  other  conditions  at  least  equal  in 
severity  to  those  of  the  work  proposed.  , 

9.  Packages. — The  cement  shall  be  delivered  in  sacks,  bar- 
rels, or  other  suitable  packages  (to  be  specified  by  the  engineer), 


SPECIFICATIONS  373 

and  shall  be  dry  and  free  from  lumps.  Each  package  shall  be 
plainly  labelled  with  the  name  of  the  brand  and  of  the  manufac- 
turer. A  sack  of  cement  shall  contain  94  pounds  net.  A  barrel 
shall  contain  376  pounds  net.  Any  package  that  is  short  weight 
or  broken,  or  that  contains  damaged  cement,  may  be  rejected, 
or  accepted  as  a  fractional  package,  at  the  option  of  the  engineer. 
If  the  cement  is  delivered  in  cloth  sacks,  the  sacks  used  shall  be 
strong  and  serviceable  and  securely  tied,  and  the  empty  sacks 
will,  if  practicable,  be  returned  to  the  contractor  at  the  point 
of  delivery  of  the  cement.  On  final  settlement  under  the  con- 
tract, ten  cents  will  be  paid  the  contractor  for  each  sack  furnished 
by  him  in  accordance  with  the  above  requirements  and  not  re- 
turned in  serviceable  condition. 

10.  Inspection. — The  cement  shall  be  tested  in  accordance 
with  the  standard  methods  hereinafter  prescribed.    In  general 
the  cement  will  be  inspected  and  tested  after  delivery,  but  partial 
or  complete  inspection  at  the  mill  may  be  called  for  in  the  speci- 
fications or  contract.     Tests  may  be  made  to  determine  the 
chemical  composition,  specific  gravity,  fineness,  soundness,  time 
of  setting,  and  tensile  strength,  and  a  cement  may  be  rejected  in 
case  it  fails  to  meet  any  of  the  specified  requirements.    An  agent 
of  the  contractor  may  be  present  at  the  making  of  the  tests  or 
they  may  be  repeated  in  his  presence. 

11.  Sampling. — The  selection  of  the  samples  for  testing  will 
be  left  to  the  engineer.    The  number  of  packages  sampled  and 
the  quantity  to  be  taken  from  each  package  will  depend  on  the 
importance  of  the  work,  the  number  of  tests  to  be  made,  and  the 
facilities  for  making  them.    The  samples  should  be  so  taken  as 
to  represent  fairly  the  material,  and,  where  conditions  permit, 
at  least  one  barrel  in  every  fifty  should  be  sampled.     Before 
tests  are  made,  samples  shall  be  passed  through  a  sieve  having 
twenty  meshes  per  linear  inch  to  remove  foreign  material.    Sam- 
ples shall  be  tested  separately  for  physical  qualities,  but  for 
chemical  analysis  mixed  samples  may  be  used.    Every  sample 
should  be  tested  for  soundness,  but  the  number  of  tests  for 
other  qualities  will  be  left  to  the  discretion  of  the  engineer. 

12.  Chemical  Analysis. — The  method  to  be  followed  for  the 
analysis  of  cement  shall  be  that  proposed  by  the  Committee  on 


374  WORKING  DATA  FOR   IRRIGATION  ENGINEERS 

Uniformity  in  the  Analysis  of  Materials  for  the  Portland  Cement 
Industry,  reported  in  Tlie  Journal  of  the  Society  for  Chemical 
Industry,  Vol.  21,  p.  12,  1902,  and  published  in  Engineering 
News,  Vol.  50,  p.  60,  1903,  and  in  The  Engineering  Record,  Vol. 
48,  p.  49,  1903.  The  insoluble  residue  shall  be  determined  on  a 
1-gram  sample,  which  is  digested  on  the  steam  bath  in  hydro- 
chloric acid  of  approximately  1.035  specific  gravity  until  the 
cement  is  dissolved.  The  residue  is  filtered,  washed  with  hot 
water,  and  the  filter-paper  contents  digested  oh  the  steam  bath 
in  a  5-per-cent  solution  of  sodium  carbonate.  The  residue  is 
then  filtered,  washed  with  hot  water,  then  with  hot  hydrochloric 
acid,  approximately  of  1.035  specific  gravity,  and  finally  with 
hot  water,  then  ignited  and  weighed.  The  quantity  so  obtained 
is  the  insoluble  residue. 

13.  Determination  of  Specific  Gravity. — The  determination 
of  specific  gravity  may  be  made  with  a  standardized  apparatus 
of  Le  Chatelier  or  other  equally  accurate  form.  Benzine  (62° 
Baume  naphtha),  or  kerosene  free  from  water,  should  be 
used  in  making  the  determination.  The  cement  should  be 
allowed  to  pass  slowly  into  the  liquid  of  the  volumenometer, 
taking  care  that  the  powder  does  not  adhere  to  the  sides  of  the 
graduated  tube  above  the  liquid  and  that  the  funnel  through 
which  it  is  introduced  does  not  touch  the  liquid.  The  tem- 
perature of  the  liquid  in  the  flask  should  not  vary  more  than  1° 
F.  during  the  operation.  To  this  end  the  flask  should  be  im- 
mersed in  water.  The  results  of  repeated  tests  should  agree 
within  0.01.*  If  the  specific  gravity  of  the  cement  as  received 
is  less  than  3.10,  a  redetermination  may  be  made  as  follows: 
Seventy  grams  of  the  cement  is  placed  in  a  nickel  or  platinum 
crucible  about  2  inches  in  diameter  and  heated  for  thirty  minutes 

*  Under  the  metric  system  the  specific  gravity  of  a  solid  is  expressed  math- 
ematically by  the  weight  in  grams  of  1  cubic  centimeter  of  the  substance  of 
the  solid.  Therefore,  in  using  a  volumenometer  graduated  to  show  volume, 
or  displacement,  in  cubic  centimeters: 

Weight  of  substance  used,  in  grams 

Specific  gravity  =  — — - —        — : — : — 

Displacement  in  cubic  centimeters. 

In  the  standard  Le  Chatelier  volumenometer  64  grams  of  Portland  cement 
are  taken. 


SPECIFICATIONS  375 

at  a  temperature  between  419°  C.  and  630°  C.  After  the  cement 
has  cooled  to  atmospheric  temperature  the  specific  gravity  shall 
be  determined  in  the  same  manner  as  described  above.  The 
cement  should  be  heated  in  a  muffle  or  other  suitable  furnace, 
the  temperature  of  which  is  to  be  maintained  above  the  melting 
point  of  zinc  (419°  C.)  but  below  the  melting  point  of  antimony 
630°  C.)-  This  maximum  temperature  can  be  recognized  as  a 
very  dull  red  which  is  just  discernible  in  the  dark. 

14.  Determination  of  Fineness. — The  No.  100  and  No.  200 
sieves  shall  conform  to  the  standard  sieve  specifications  of  the 
Bureau  of  Standards,  Department  of  Commerce.     The  deter- 
mination  of  fineness  should  be  made  on  a  50-gram  sample, 
which  may  be  dried  at  a  temperature  of  100°  C.  (212°  F.),  prior 
to  sifting.     The  coarsely  screened  sample  should  be  weighed 
and  placed  on  the  No.  200  sieve,  which,  with  the  pan  and  cover 
attached,  should  beheld  in  one  hand  hi  a  slightly  inclined  position 
and  moved  forward  and  backward  in  the  plane  of  inclination,  at 
the  same  time  striking  the  side  gently  about  200  times  per  minute 
against  the  palm  of  the  other  hand  on  the  upstroke.    The  oper- 
ation is  to  be  continued  until  not  more  than  0.05  gram  will  pass 
through  in  one  minute.    The  residue  should  be  weighed,  then 
placed  on  the  No.  100  sieve,  and  the  operation  repeated.    The 
sieves  should  be  thoroughly  dry  and  clean.    Determination  of 
fineness  may  be  made  by  washing  the  cement  through  the  sieve 
or  by  a  mechanical  sifting  device  which  has  been  previously 
standardized  with  the  results  obtained  by  hand  sifting  on  equiv- 
alent samples.    In  case  of  the  failure  of  the  cement  to  pass  the 
fineness  requirements  by  the  washing  method  or  the  mechanical 
device,  it  shall  be  tested  by  hand. 

15.  Mixing  Cement  Pastes  and  Mortars. — The  quantity  of 
cement  or  cement  and  sand  to  be  used  in  the  paste  or  mortar 
should  be  expressed  in  grams  and  the  quantity  of  water  in  cubic 
centimeters.     The  material  should  be  weighed,  placed  upon  a 
non-absorbent  surface,  thoroughly  mixed  dry  if  sand  be  used,  and 
a  crater  formed  in  the  center,  into  which  the  proper  percentage  of 
clean  water  should  be  poured;  the  material  on  the  outer  edge 
should  be  turned  into  the  crater  by  the  aid  of  a  trowel.    As  soon 
as  the  water  has  been  absorbed,  the  operation  should  be  completed 


376  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

by  vigorously  mixing  with  the  hands  for  one  minute  and  a  half. 
During  the  operation  of  mixing,  the  hands  should  be  protected 
by  rubber  gloves.  The  temperature  of  the  room  and  the  mixing 
water  should  be  maintained  as  nearly  as  practicable  at  21°  C. 
(70°  F.). 

1  6.  Determination  of  Normal  Consistency.  —  The  normal 
consistency  for  neat  paste  to  be  used  in  making  briquettes  and 
pats  should  be  determined  by  the  ball  method,  as  follows:  A 
quantity  of  cement  paste  should  be  mixed  in  the  manner  de- 
scribed in  paragraph  15,  and  quickly  formed  into  a  ball  about 
2  inches  in  diameter.  The  ball  should  then  be  dropped  upon  a 
hard,  smooth,  and  flat  surface  from  a  height  of  2  feet.  The  paste 
is  of  normal  consistency  when  the  ball  does  not  crack  and  does 
not  flatten  more  than  one-half  of  its  original  diameter.  Trial 
pastes  should  be  made  with  varying  percentages  of  water,  until 
the  correct  consistency  is  obtained.  The  percentage  of  water  to 
be  used  in  mixing  mortars  for  sand  briquettes  is  given  by  the 
formula: 


in  which  y  is  the  percentage  of  water  required  for  the  sand  mortar; 
P  is  the  percentage  of  water  required  for  neat  cement 

paste  of  normal  consistency; 
n  is  the  number  of  parts  of  sand  to  one  of  cement  by 

weight,  and 
K  is  a  constant  which  for  standard  Ottawa  sand  has  the 

value  of  6.5. 

The  percentage  of  water  to  be  used  for  mortars  containing 
three  parts  standard  Ottawa  sand,  by  weight,  to  one  of  cement 
is  indicated  in  the  following  statement: 


Percentage 
of  Water 
for  Neat 
Cement  Paste 

18  

Percentage  of  Water 
for  1  to  3 
Mortars  of  Standard 
Ottawa  Sand 

9.5 

Percentage 
of  Water 
for  Neat 
Cement  Paste 

24  

Percentage  of  Water 
for  1  to  3 
Mortars  of  Standard 
Ottawa  Sand 

10  5 

19  

9.7 

25.    ... 

10  7 

20  

9.8 

26 

10  8 

21.  

10  0 

27 

11  0 

22  

.  .    .           10  2 

28 

11  2 

23.. 

..10.3 

29.. 

..11.3 

SPECIFICATIONS  377 

17.  Determination  of  Soundness. — Pats  of  neat  cement  paste 
of  normal  consistency  about  3  inches  in  diameter,  J^  inch  in 
thickness  at  the  center,  and  tapering  to  a  thin  edge,  should  be 
kept  in  moist  air  for  a  period  of  twenty-four  hours.     One  pat 
should  then  be  kept  in  air  and  a  second  in  water,  at  the  ordinary 
temperature  of  the  laboratory  not  to  vary  greatly  from  21°  C. 
(70°  F.),  and  both  observed   at  intervals   for  at  least  twenty- 
eight  days.    A  third  pat  should  be  exposed  to  steam  at  atmos- 
pheric pressure  above  boiling  water  for  five  hours. 

18.  Determination  of  Time  of  Setting. — The  time  of  setting 
should  be  determined  by  the  standardized  Gilmore*  needles,  as 
follows:  A  pat  of  neat  cement  paste  about  3  inches  in  diameter 
and  y^  inch  in  thickness  with  flat  top,  mixed  at  normal  con- 
sistency, should  be  kept  in  moist  air,  at  a  temperature  main- 
tained   as    nearly    as    practicable    at   21°   C.    (70°  F.).    The 
cement  is  considered  to  have  acquired  its  initial  set  when  the 
pat  will  bear,  without  appreciable  indentation,  a  needle  /fc  of  an 
inch  in  diameter  loaded  to  weigh  J^  of  a  pound.    The  final  set 
has  been  acquired  when  the  pat  will  bear,  without  appreciable 
indentation,  a  needle  /24  of  an  inch  in  diameter,  loaded  to  weigh 
1  pound.     In  making  the  test  the  needle  should  be  held  in  a 
vertical  position  and  applied  lightly  to  the  surface  of  the  pat. 
The  pats  made  for  the  soundness  test  may  be  used  to  determine 
the  time  of  setting. 

19.  Tensile  Tests. — Tensile  tests  should  be  made  on  an 
approved  machine.     The  test  pieces  shall  be  briquettes  of  the 
form  recommended  by  the  Committee  on  Uniform  Tests  of 
Cement  of  the  American  Society  of  Civil  Engineers,  and  illus- 
trated in  Circular  33  of  the  Bureau  of  Standards.    The  briquettes 
shall  be  made  of  paste  or  mortar  of  normal  consistency.    Imme- 
diately after  mixing,  the  paste  or  mortar  should  be  placed  in 
the  moulds,  pressed  in  firmly  by  the  fingers  and  smoothed  off 
with   a   trowel   without   mechanical   ramming.     The   material 
should  be  heaped  above  the  mould,  and,  in  smoothing  off,  the 
trowel  should  be  drawn  over  the  mould  in  such  a  manner  as  to 
exert  a  moderate  pressure  on  the  material.    The  moulds  should  be 

*  The  Gilmore  needle  is  specified  in  Government  specifications.     Other 
specifications  specify  the  Vicat  needle. 


378  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

turned  over  and  the  operation  of  heaping  and  smoothing  off 
repeated.  Not  less  than  three  briquettes  should  be  made  and 
tested  for  each  sample  for  each  period  of  test.  The  neat  tests 
are  not  considered  as  important  as  the  sand  tests.  The  briquettes 
should  be  broken  as  soon  as  they  are  removed  from  the  water. 
The  load  should  be  applied  at  the  rate  of  600  pounds  per  minute. 

20.  Storage  of  Test  Pieces. — During  the  first  twenty-four 
hours  after  moulding  the  test  pieces  should  be  kept  in  air  suffi- 
ciently moist  to  prevent  them  from  drying.    After  twenty-four 
hours  in  moist  air  the  test  pieces  should  be  immersed  in  water. 
The  air  and  water  should  be  maintained  as  nearly  as  practical 
at21°C.  (70°  F.). 

21.  Standard  Sand. — The  sand  to  be  used  shall  be  natural 
sand  from  Ottawa,  Illinois,  screened  to  pass  a  No.  20  sieve  and 
retained  on  a  No.  30  sieve.    Sand  having  passed  the  No.  20  sieve 
shall  be  considered  standard  when  not  more  than  2  grams  pass 
the  No.  30  sieve  after  one  minute  continuous  sifting  of  a  200- 
gram  sample.    The  No.  20  and  No.  30  sieves  shall  conform  to  the 
standard  sieve  specifications  of  the  Bureau  of  Standards,  Depart- 
ment of  Commerce. 

SPECIFICATIONS  FOR  TIMBER  PILES 

i.  Timber  Piles. — Piles  shall  be  cut  from  sound  trees;  shall 
be  close-grained  and  solid;  free  from  injurious  ring  shakes,  large 
and  unsound  or  loose  knots,  decay,  or  other  defects  that  may 
materially  impair  their  strength  or  durability.  The  piles  shall  be 
cut  above  the  ground  swell  and  have  a  uniform  taper  from  butt 
to  tip.  Short  bends  or  bends  in  two  directions  will  not  be  al- 
lowed. A  line  drawn  from  the  center  of  the  butt  to  the  center 
of  the  tip  shall  lie  wholly  within  the  body  of  the  pile.  Piles  shall 
be  peeled  soon  after  cutting.  All  knots  shall  be  trimmed  close 
to  the  body  of  the  pile.  The  minimum  diameter  at  the  tip 
shall  be  9  inches  for  lengths  not  exceeding  30  feet,  8  inches  for 
lengths  over  30  feet  but  not  exceeding  50  feet,  and  7  inches  for 
lengths  over  50  feet.  The  minimum  diameter  at  one-quarter  of 
the  length  from  the  butt  shall  be  12  inches  and  the  maximum 
diameter  at  the  butt  20  inches.  (Note. — The  kind  of  timber  to 
be  specified  depends  upon  the  locality.} 


SPECIFICATIONS  379 

SPECIFICATIONS  FOR  STRUCTURAL  STEEL 

(Based  on  "  Standard  Specifications  for  Structural  Steel  for 
Buildings"  of  the  American  Society  for  Testing  Materials, 
adopted  August  25,  1913.) 

1.  Manufacture. — Structural  steel  may  be  made  by  either 
the  open-hearth  or  Bessemer  process.    Rivet  steel  and  plate  or 
angle  material  over  %  inch  thick,  which  is  punched,  shall  be 
made  by  the  open-hearth  process.    The  steel  shall  conform  in  all 
respects,  not  specifically  mentioned  herein,  to  the  "  Standard 
Specifications  for  Structural  Steel  for  Buildings  "  of  the  American 
Society  for  Testing  Materials,  adopted  August  25,  1913,  and 
tests  shall  be  made  as  provided  in  said  specifications. 

2.  Chemical  and  Physical  Properties  of  Structural  Steel. — 
Steel  made  by  the  Bessemer  process  shall  contain  not  more  than 
0.10  per  cent  phosphorus  and  steel  made  by  the  open-hearth 
process  shall  contain  not  more  than  0.06  per  cent  phosphorus. 
All  structural  steel  shall  have  an  ultimate  tensile  strength  of 
55,000  to  65,000  pounds  per  square  inch;  an  elastic  limit,  as 
determined  by  the  drop  of  the  beam,  of  not  less  than  one-half 
the  ultimate  tensile  strength;  a  minimum  per  cent  of  elongation 
in  8  inches  of  1,400,000  divided  by  the  ultimate  tensile  strength; 
a  silky  fracture;  and  capability  of  being  bent  cold  without 
fracture    180°  flat  on   itself  for   J^-inch  material  and  under; 
around  a  pin  having  a  diameter  equal  to  the  thickness  of  the 
test  piece  for  material  over  %  inch  to  and  including  1^  inches; 
and  around  a  pin  having  a  diameter  equal  to  twice  the  thickness 
of  the  test  piece  for  material  over  1J4  inches  in  thickness.    A 
deduction  of  1  from  the  specified  percentage  of  elongation  will 
be  allowed  for  each  %  inch  in  thickness  above  %  inch;    and  a 
deduction  of  2.5  will  be  allowed  for  each  /{6  inch  in  thickness 
below  %Q  inch. 

3.  Chemical  and  Physical  Properties  of  Rivet  Steel. — Rivet 
steel  shall  contain  not  more  than  0.06  per  cent  phosphorus  nor 
more  than  0.045  per  cent  sulphur.     It  shall  have  an  ultimate 
tensile  strength  of  48,000  to  58,000  pounds  per  square  inch;  an 
elastic  limit  of  one-half  the  ultimate  tensile  strength;  a  mini- 
mum per  cent  of  elongation  in  8  inches  of  1,400,000  divided  by 


380  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

the  ultimate  tensile  strength;  a  silky  fracture;  and  capability  of 
being  bent  cold  without  fracture  180°  flat  on  itself. 

4.  Finish. — Finished  material  must  be  free  from  injurious 
seams,  flaws,  or  cracks,  and  have  a  workmanlike  finish. 

5.  Marking. — Every  finished  piece  of  steel  shall  be  stamped 
with  the  melt  or  blow  number,  except  that  small  pieces  may  be 
shipped  in  bundles  securely  wired  together  with  the  melt  or  blow 
number  on  a  metal  tag  attached. 

6.  Test  Pieces. — (This    paragraph    should  state   who   is   to 
furnish  test  pieces,  what  disposition  is  to  be  made  of  broken  test 
specimens,  etc.) 

7.  Tests. — (This  paragraph  should  state  who  will  make  tests, 
at  whose  expense  tests  will  be  made,  etc.) 

8.  Shipment. — 

9.  Payment.— 

SPECIFICATIONS   FOR   STEEL   REINFORCEMENT 

BARS 

(Based  on  "  Standard  Specifications  for  Billet-Steel  Concrete  Re- 
inforcement Bars  "  of  the  American  Society  for  Testing  Ma- 
terials, adopted  August  25,  1913.) 

1.  Manufacture. — Steel  may  be  made  by  either  the  open- 
hearth  or  Bessemer  process  and  the  bars  shall  be  rolled  from 
billets.     It  shall  conform  in  all  respects,  not  specifically  men- 
tioned herein,  to  the  "Standard  Specifications  for  Billet-Steel 
Concrete  Reinforcement  Bars  "   of  the  American  Society  for 
Testing  Materials  adopted  August  25,  1913,  and  tests  shall.be 
made  as  provided  in  said  specifications. 

2.  Type  of  Bars. — All  reinforcement  bars  shall  be  of   the 
deformed  type.     Bidders  shall  submit  samples  or  cuts  of  the 
type  of  bar  they  propose  to  furnish. 

3.  Chemical  Properties. — Bars  of  steel  made  by  the  Besse- 
mer process  shall  contain  not  more  than  0.10  per  cent  phosphorus, 
and  not  more  than  0.05  per  cent  phosphorus  if  made  by  the  open- 
hearth  process. 

4.  Physical  Properties. — Bars  of  steel  shall  have  an  ultimate 
tensile  strength  of  55,000  to  70,000  pounds  per  square  inch;  an 
elastic  limit  of  not  less  than  33,000  pounds  per  square  inch;  a 


SPECIFICATIONS  381 

minimum  per  cent  of  elongation  in  8  inches  of  1,250,000  divided 
by  the  ultimate  tensile  strength;  and  capability  of  being  bent 
cold  without  fracture  180°  around  a  pin  having  a  diameter 
equal  to  the  thickness  of  the  test  piece  for  material  less  than 
%  inch  in  thickness,  and  around  a  pin  having  a  diameter  equal 
to  twice  the  thickness  of  the  test  piece  for  material  of  %  mcri  and 
over  in  thickness.  For  each  increase  of  ^  inch  in  diameter  or 
thickness  above  M  inch  and  for  each  decrease  of  /{6  inch  in  di- 
ameter or  thickness  below  /(e  inch,  a  deduction  of  1  will  be 
allowed  from  the  specified  percentage  of  elongation. 

5.  Variation  in  Weight. — Bars  for  reinforcement  are  subject 
to  rejection  if  the  actual  weight  of  any  lot  varies  more  than 
5  per  cent  over  or  under  the  theoretical  weight  of  that  lot. 

6.  Finish. — Finished  material  shall  be  free  from  injurious 
seams,  flaws,  or  cracks,  and  shall  have  a  workmanlike  finish. 

7.  Test  Pieces.— (See  "  Structural  Steel.") 

8.  Tests.— (See  " Structural  Steel") 

9.  Shipment  — 
10.  Payment. — 

SPECIFICATIONS   FOR  GRAY-IRON  CASTINGS 

(Based  on  "  Standard  Specifications  for  Gray-Iron  Castings  "  of 
the  American  Society  for  Testing  Materials,  adopted  Sep- 
tember 1,  1903.) 

1.  Manufacture. — Castings  shall  be  of  tough  gray  iron  made 
by  the  cupola  process.    In  all  respects,  not  specifically  mentioned 
herein,  the  castings  shall  conform  to  the  "  Standard  Specifica- 
tions for   Gray-Iron   Castings  "   of  the  American   Society  for 
Testing  Materials,  adopted  September  1,  1901,  and  tests  shall 
be  made  as  provided  in  said  specifications. 

2.  Light  Castings,  Physical  and  Chemical  Properties. — Cast- 
ings having  any  section  less  than  J/£  inch  thick  shall  be  known 
as  light  castings.    The  sulphur  content  shall  be  not  greater  than 
0.08  per  cent.    The  minimum  breaking  load  of  a  bar  l^t  inches 
in  diameter,  loaded  at  the  middle  of  a  12-inch  span,  shall  be 
2,500  pounds.    The  deflection  shall  in  no  case  be  less  than  0.1  inch. 

3.  Heavy  Castings,   Physical  and   Chemical  Properties. — 
Castings  in  which  no  section  is  less  than  2  inches  thick  shall  be 


382  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

known  as  heavy  castings.  The  sulphur  content  shall  be  not 
greater  than  0.12  per  cent.  The  minimum  breaking  load  of  a 
bar  1J4  inches  in  diameter,  loaded  at  the  middle  of  a  12-inch 
span,  shall  be  3,300  pounds.  The  deflection  shall  in  no  case  be 
less  than  0.1  inch. 

4.  Medium  Castings,  Physical  and  Chemical  Properties. — 
Medium  castings  are  those  not  included  under  "  light "   or 
"  heavy  "  castings.    Their  sulphur  content  shall  be  not  greater 
than  0.10  per  cent.    The  minimum  breaking  load  of  a  bar  1}^ 
inches  in  diameter  loaded  at  the  middle  of  a  12-inch  span  shall 
be  2,900  pounds.    The  deflection  shall  in  no  case  be  less  than  0.1 
inch. 

5.  Finish. — All  castings  shall  be  true  to  pattern,  free  from 
cracks,   flaws,   porosity,    cold-shuts,  blow-holes,  and   excessive 
shrinkage  and  shall  have  a  workmanlike  finish. 

6.  Test  Pieces.— (See  "Structural  Steel.") 

7.  Tests.— (See  "Structural  Steel") 

8.  Shipment.— 

9.  Payment. — 

SPECIFICATIONS   FOR   MALLEABLE   CASTINGS 

(Based  on  "  Standard  Specifications  for  Malleable  Castings  "  of 
the  American  Society  for  Testing  Materials,  adopted  Novem- 
ber 15,  1904.) 

1.  Manufacture. — Malleable  iron  castings  may  be  made  by 
the  open-hearth  or  air-furnace  process.     In  all  respects  not 
specifically  mentioned  herein  the  castings  shall  conform  to  the 
"  Standard  Specifications  for  Malleable  Castings  "  of  the  Ameri- 
can Society  for  Testing  Materials,  adopted  November  15,  1904, 
and  tests  shall  be  made  as  provided  in  said  specifications. 

2.  Chemical  and  Physical  Properties. — Castings  shall  con- 
tain not  more  than  0.06  per  cent  of  sulphur  nor  more  than  .0225 
per  cent  of  phosphorus.    They  shall  have  a  tensile  strength  of 
not  less  than  40,000  pounds  per  square  inch  and  the  elongation 
measured  in  2  inches  shall  be  not  less  than  2j/£  per  cent.    The 
transverse  strength  of  the  standard  test  bar  1  inch  square,  loaded 
at  the  middle  of  a  12-inch  span,  shall  be  not  less  than  3,000 
pounds  per  square  inch;  and  the  deflection  shall  be  at  least  %  mcn- 


SPECIFICATIONS  383 

3.  Finish. — Castings  shall  be  true  to  pattern,  free  from  blem- 
ishes, scale,  and  shrinkage  cracks,  and  shall  have  a  workmanlike 
finish. 

4.  Test  Pieces.— (See  "Structural  Steel.") 

5.  Tests.— (See  "Structural  Steel.") 

6.  Shipment. — 

7.  Payment— 

SPECIFICATIONS  FOR   STEEL   CASTINGS 

(Based  on  "  Standard  Specifications  for  Steel  Castings  "  of  the 
American  Society  for  Testing  Materials,  adopted  August  25, 
1913.) 

1.  Manufacture. — Steel  for  castings  may  be  made  by  the 
open-hearth,  crucible,  or  Bessemer  process.     Castings  shall  be 
annealed  unless  otherwise  specified,   and  in  all  respects  not 
specifically  mentioned  herein  their  material  and  manufacture 
shall  conform  to  the  "  Standard  Specifications  for  Steel  Castings 
of  the  American  Society  for  Testing  Materials,"  adopted  August 
25,  1913,  and  tests  shall  be  made  as  provided  in  said  specifica- 
tions. 

2.  Chemical  and  Physical  Properties. — Castings  shall  con- 
tain not  more  than  0.05  per  cent  of  phosphorus  nor  more  than 
0.05  per  cent  of  sulphur.    Castings  shall  be  classed  as  "  Hard," 
"  Medium,"  and  "  Soft,"  and  shall  have  the  following  physical 
properties : 


Tensile  strength,  pounds  per  square  inch 
Elastic  limit  

Hard 

80,000 
36,000 

Medium 
70,000 
31,500 

Soft 
60,000 
27,000 

Elongation,  per  cent  in  2  inches     .    . 

15 

18 

22 

Contraction  of  area,  oer  cent.  . 

20 

25 

30 

3.  Finish. — Castings   shall  be   true   to  pattern,   free  from 
blemishes,  flaws,  or  shrinkage  cracks.    Bearing  surfaces  shall  be 
solid  and  no  porosity  shall  be  allowed  in  positions  where  the 
resistance  and  value  of  the  casting  for  the  purpose  intended  will 
be  seriously  affected  thereby. 

4.  Test  Pieces.— (See  "Structural  Steel.") 

5.  Tests.— (See  "Structural  Steel.") 

6.  Shipment. — 

7.  Payment. — 


384  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

SPECIFICATIONS  FOR  FORGED   OR  ROLLED 
BRONZES 

(Use  of  Forged  or  Rolled  Bronzes) 

(a)  Class  A  and  No.  1    manganese    bronze    have    the    same 
physical  properties,  but  the  manganese  bronze  is  generally  more 
reliable  and  also  more  expensive. 

(b)  No.  2  and  No.  3  manganese  bronze  are  adaptable  where 
greater  strength  is  required  than  is  furnished  by  No.  1,  but  they 
are  less  ductile. 

(c)  Phosphor  bronze  is  valuable  where  non-corrodibility  is  an 
important  item,  but  should  not  be  used  where  great  strength  and 
ductility  are  essential. 

(d)  Tobin  bronze  is  valuable  for  shafting,   bolts,   nuts,   and 
other  fastenings  where  a  high  degree  of  non-corrodibility  is  essen- 
tial.    It  is  more  easily  forged  and  stamped  than  any  of  the  other 
bronzes. 

1.  Kind  and  Quality. — Forged  or  rolled  bronze  shall  be  made 
of  new  metal  of  the  best  grade  as  to  purity  and  homogeneity. 
The  use  of  scrap  bronze  will  not  be  allowed. 

2.  Shapes. — Forged  or  rolled  bronze  pieces  shall  be   accu- 
rately formed  as  shown  on  the  drawings.    The  contractor  will  be 
held  responsible  for  the  correct  fitting  of  the  parts  designed  to 
conform  one  with  the  other,  so  that  the  whole  may  be  properly 
assembled  in  good  working  order. 

3.  Annealing. — Cold  working  of  bronze  shall  be  avoided  if 
possible,  but  when  cold  working  is  necessary  the  material  shall 
be  subsequently  annealed. 

4.  Physical  Properties  of  Class  A  Bronze. — Class  A  bronze 
shall  have  the  following  physical  properties :  An  ultimate  tensile 
strength  in  pounds  per  square  inch  of  not  less  than  60,000;  an 
elastic  limit  of  not  less  than  one-half  the  ultimate  tensile  strength; 
and  a  minimum  per  cent  of  ultimate  elongation  in  2  inches  of  30. 

5.  Physical  Properties  of  No.  i  Manganese  Bronze. — No.  1 
manganese  bronze  shall  have  the  following  physical  properties: 
An  ultimate  tensile  strength  in  pounds  per  square  inch  of  not  less 
than  60,000;  an  elastic  limit  of  not  less  than  one-half  the  ultimate 
tensile  strength;  a  minimum  per  cent  of  ultimate  elongation  in 
2  inches  of  30. 


SPECIFICATIONS  385 

6.  Physical  Properties  of  No.  2  Manganese  Bronze. — No.  2 

manganese  bronze  shall  have  the  following  physical  properties: 
An  ultimate  tensile  strength  in  pounds  per  square  inch  of  not  less 
than  70,000;  an  elastic  limit  of  not  less  than  one-half  the  ultimate 
tensile  strength;  and  a  minimum  per  cent  of  ultimate  elongation 
in  2  inches  of  28. 

7.  Physical  Properties  of  No.  3  Manganese  Bronze. — No.  3 
manganese  bronze  shall  have  the  following  physical  properties: 
An  ultimate  tensile  strength  in  pounds  per  square  inch  of  not  less 
than  80,000;  an  elastic  limit  of  not  less  than  one-half  the  ultimate 
tensile  strength;  and  a  minimum  per  cent  of  ultimate  elongation 
in  2  inches  of  25. 

8.  Physical  and  Chemical  Properties  of  Phosphor  Bronze. — 
Phosphor  bronze  shall  have  the  following  physical  properties: 
An  ultimate  tensile  strength  in  pounds  per  square  inch  of  not 
less  than  50,000;  an  elastic  limit  of  not  less  than  one-half  the 
ulmtiate  tensile  strength;  and  a  minimum  per  cent  of  ultimate 
elongation  in  2  inches  of  25.     Chemical  analyses  of  phosphor 
bronze  shall  show:   Copper,  79  to  81  per  cent;  tin,  9  to  11  per 
cent;  lead,  9  to  11  per  cent;  phosphorus,  0.7  to  1.0  per  cent. 
The  analyses  shall  show  not  more  than  1  per  cent  of  all  other 
ingredients  combined. 

9.  Physical  and  Chemical  Properties  of  Tobin  Bronze. — 
Tobin  bronze  shall  have  the  following  physical  properties:    An 
ultimate  tensile  strength  of  60,000  pounds  per  square  inch;  an 
elastic  limit  of  not  less  than  one-half  the  ultimate  tensile  strength; 
a  minimum  per  cent  of  ultimate  elongation  in  2  inches  of  30.    A 
chemical  analysis  of  the  composition  of  Tobin  bronze  shall  show 
the  following  per  cents  of  materials:  59  to  63  per  cent  of  copper; 
0.5  to  1.5  per  cent  of  tin;  the  remainder  of  zinc,  with  such  small 
percentage  of  other  ingredients  as  the  manufacturer  considers 
best  suited  to  produce  the  specified  physical  properties  and  in- 
corrodibility. 

10.  Finish. — Finished  pieces  of  bronze  shall  be  free  from 
injurious  seams,  flaws,  and  cracks,  and  shall  have  a  workmanlike 
finish. 

n.   Markings. — Large   pieces   of   finished   bronze   shall   be 
stamped  with  the  melt  number;  and  small  pieces  may  be  tied  in 


386  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

suitable  packages  or  bundles,  securely  wired  together,  having 
the  melt  number  on  attached  tags. 

12.  Test  Pieces. — The  contractor  shall  furnish  at  his  own 
expense  all  test  pieces.    At  least  one  test  piece  shall  be  taken 
from  each  melt  of  bronze.    The  standard  test  pieces  shall  be  cut 
from  the  finished  material  or  from  material  from  the  same  melt 
and  treated  in  exactly  the  same  manner.    The  test  pieces  shall 
be  J^  inch  in  diameter  and  shall  have  2  inches  of  gage  length, 
except  that  large  bars  may  be  tested  in  full  sizes.    All  test  bars 
and  test  pieces  shall  be  marked  so  as  to  indicate  clearly  the 
material  they  represent  and  shall  be  properly  boxed  and  prepared 
for  shipment  if  required. 

13.  Tests.— (See  "Structural  Steel.") 

14.  Shipment.— 

15.  Payment.— 

SPECIFICATIONS  FOR   CAST  BRONZES 

(Use  of  Cast  Bronzes) 

(a)  Class  A  bronze  is  adaptable  for  castings  where  physical 
rather  than  chemical  properties  are  the  more  important. 

(b)  Class  B    bronze   is    adaptable  for    bearings,    bushings, 
sleeves,  and  all  parts  subject  to  considerable  wear. 

(c)  Class  C  and  Class  D  bronze  are  especially  adaptable  to 
sliding  surfaces  in  contact,  such  as  bearing  faces   of  gates  and 
gate  frames,  Class  C  being  used  for  one  bearing  and  Class  D  for 
the  other  bearing  in  contact  therewith. 

(d)  Manganese  bronze  is  valuable  for  its  physical  properties 
and  is  generally  more  expensive,  but  stronger  and  more  reliable 
than  Class  A  bronze. 

(e)  Phosphor  bronze  is  adaptable   where  non-corrodibility  is 
an  important  factor.     It  is  slow  to  heat  and  is  a  good  bearing 
metal. 

i.  Kind  and  Quality. — Castings  of  bronze  shall  be  made  of 
new  metal,  and  shall  have  a  homogeneous  structure  free  from 
cold  shuts,  blow-holes,  porosity,  flaws,  patching,  plugging,  and 
other  injurious  imperfections.  The  use  of  bronze  scrap  will  not 
be  allowed. 


SPECIFICATIONS  387 

2.  Castings. — Castings  shall  have  the  forms  and  dimensions 
shown  in  the  drawings.    The  contractor  will  be  held  responsible 
for  correct  fitting  of  the  parts  designed  to  conform  one  with 
the  other,  so  that  the  whole  may  be  properly  assembled  in  good 
working  order. 

3.  Physical  Properties  of  Class  A  Bronze. — Class  A  bronze 
must  have  the  following  properties:  An  ultimate  tensile  strength 
in  pounds  per  square  inch  of  not  less  than  60,000;  an  elastic 
limit  of  not  less  than  one-half  the  ultimate  tensile  strength;  and 
a  minimum  per  cent  of  ultimate  elongation  in  2  inches  of  15. 

4.  Chemical  Properties  of  Class  B  Bronze. — Chemical  an- 
alyses of  the  composition  of  Class  B  bronze  shall  show  from  82 
to  84  per  cent  of  copper,  12J/2  to  14 J^  per  cent  of  tin,  and  2j/£  to 
4j/£  per  cent  of  zinc. 

5.  Chemical  Properties  of  Class  C  and  Class  D  Bronze. — 
Class  C  bronze  shall  have  the  following  chemical  composition: 
Copper,  82.7  per  cent;  lead,  4.9  per  cent;  zinc,  5.3  per  cent;  and 
tin,  7.1  per  cent.    Class  D  bronze  shall  have  the  following  chem- 
ical composition:  Copper,  82.8  per  cent;  lead,  8.0  per  cent;  zinc, 
4.4  per  cent;  tin,  4.8  per  cent. 

6.  Physical  Properties  of  Manganese  Bronze. — Manganese 
bronze  must  have  the  following  physical  properties:    Ultimate 
tensile  strength  in  pounds  per  square  inch  of  not  less  than 
60,000;  an  elastic  limit  of  not  less  than  one-half  the  ultimate 
tensile  strength;  and  a  minimum  per  cent  of  ultimate  elongation 
in  2  inches  of  20. 

7.  Physical  and  Chemical  Properties  of  Phosphor  Bronze. — 
Phosphor  bronze  must  have  the  following  physical  properties: 
An  ultimate  tensile  strength  in  pounds  per  square  inch  of  not 
less  than  25,000;  an  elastic  limit  of  not  less  than  one-half  the 
ultimate   tensile  strength;   a  minimum  per  cent  of  ultimate 
elongation  in  2  inches  of  5.    Chemical  analyses  of  the  composi- 
tion of  phosphor  bronze  shall  show:   79  to  81  per  cent  copper; 
9  to  11  per  cent  tin;  9  to  11  per  cent  lead;  and  0.7  to  1.0  per  cent 
phosphorus.     The  analyses  shall  show  not  more  than  0.5  per 
cent  of  other  ingredients. 

8.  Finish. — All  castings  shall  be  finished  true  to  pattern, 
and  shall  be  free  from  excessive  shrinkage,  porosity,  blow-holes, 


388  WORKING  DATA  FOR  IRRIGATION  ENGINEERS 

and  other  injurious  imperfections,  and  shall  have  a  workmanlike 
finish. 

9.  Markings. — Each  casting  shall  be  marked  or  tagged  with 
the  melt  number  from  which  it  is  made. 

10.  Test  Pieces. — The  contractor  shall  furnish  at  his  own 
expense  all  test  pieces.    At  least  one  test  piece  shall  be  taken 
from  each  melt  of  bronze.    The  standard  test  pieces  shall  be 
cut  from  the  finished  material  or  from  material  from  the  same 
melt  and  treated  in  exactly  the  same  manner.    The  test  pieces 
shall  be  ^  inch  in  diameter  and  shall  have  2  inches  of  gage 
length,  except  that  large  bars  may  be  tested  in  full  sizes.    All 
test  bars  and  test  pieces  shall  be  marked  so  as  to  indicate  clearly 
the  material  they  represent  and  shall  be  properly  boxed  and 
prepared  for  shipment  if  required. 

n.  Tests.— (See  "Structural  Steel.") 

12.  Shipment.— 

13.  Payment.— 


INDEX 


Acre-feet  equivalents  in  second-feet, 

194 
Allowable  depth  of  backfill  for  steel 

pipe,  244 

Allowable  stresses  in  timber,  233 
Altitudes,  dictionary  of,  1 
Areas  of  circles,  292 
Areas,  weights,  and  spacing  of  round 

and  square  bars,  230,  231 

Bars,  spacing  of,  in  reinforced  con- 
crete beams,  230,  231 
Bazin's  formula  for  rectangular  weirs, 

with  tables,  189 
Beams,  220 

bending  moments  in,  221;  table, 

223 

coefficient  of  resistance  of  rein- 
forced concrete,  229 
reinforced    concrete,    222;     dia- 
gram, 229;  spacing  of  rods  in, 
230,  231 

wooden,  values  of  M/S,  234 
Bending    moments    in    beams,    221; 

table,  223 

Bottom  width  of  canals,  46 
Broad-crested  weirs,  191,  192,  193 

Canal  locations,  general  remarks  on, 

26 
Canals,  25,  26 

bottom  width,  46 

capacity,  41,  160-165 

depth,  46 

design,  41 

diagrams  for  determining  veloc- 
ities and  slopes,  91-107 

diagrams  for  design  of  sections, 
110-147 

discharge  of  small,  160-165 

excavation  for,  203-219 

formula  for  flow,  50 

freeboard,    59;    on    curves,    60; 
formula  for,  61 


Canals,  grades,  47 

Kutter  formula,  50 

location,  25,  26 

scouring    and    silting    velocities, 

48;  tables,  49 
seepage  losses,  43;  diagram,  45; 

table,  44 
side  slopes,  44 
values  of  "C"  for,  90-109 
values  of  n,  50;  tables,  52 
velocities,  47 
Capacity  of  canals,  41 
Capacity  of  pipes, 

decrease  with  age,  69 
formulas  for,  67 
Cast-iron  pipe,  discharge,  172 
thickness  and  weight,  247 
Channels,  diagrams  for  determining 
velocities  and   slopes,   91-107 
values  of  coefficient  "C,"  90-109 
Chezy  formula,  values  of   "C,"   90- 

109 

Chutes,  design,  62 
Cippoletti  weirs,  11 
discharge,  181 

Circles,  circumference  of,  292 
Circular  conduits  flowing  partly  full, 

150-153 
Circular  segments,  hydraulic  elements 

of,  144-147 

Circumference  of  circles,  292 
Coefficient   "C"   in   Chezy   formula, 

values  of,  90-109 

Coefficient   for   discharge    of   broad- 
crested  weirs  or  dams,  191-193 
Coefficient  for  submerged  weirs,  180 
Coefficient  for  velocity  of  approach  to 

weirs,  182 
Coefficients  of  resistance  of  reinforced 

concrete  beams,  229 
Columns,   formula   for  bending  mo- 
ment, 233 

Concrete,  materials  required  for  one 
cubic  yard,  232 


389 


390 


INDEX 


Concrete  pipe,  discharge,  172 

spacing   of   reinforcement   bars, 

237,  243 
Conduits,  circular,  flowing  partly  full, 

150-153 

Contents  in  feet  B.M.  of  logs,  236 
Contents  in  feet  B.M.  of  lumber,  235 
Convenient  equivalents,  258 
Conversion  diagram,  "acres  per  sec- 
ond-foot" to  "depth  of  water," 
196 

Conversion  of  linear  units,  260 
Conversion,  English  to  metric  units, 

264 

metric  to  English  units,  262 
Conversion    table    for    acre-feet    to 

second-feet,  194 

Conversion   table,    inches   and   frac- 
tions to  decimals  of  a  foot,  259 
Correction  for  curvature  and  refrac- 
tion, 265 

Cosines,  natural,  282 
Cotangents,  natural,  284 
Cubes  of  numbers,  292 
Culverts,  design,  71 
Current  meter,  description  of,  14 
kinds  of,  14 
method  of  making  measurement 

with,  15 

Current  meter  station,  cable  for,  15 
discussion  of,  13 
discharge,     velocity,    and     area 

curves  for,  18 
gagings  at,  8 
soundings  at,  15 
Curve  formulae,  277 
Curvature  of  wood  pipe,  242 
Curvature  and  refraction,  correction 
for,  265 

Dams,  discharge  over,  191-193 
diversion  (see  Diversion  dams) 
pressure  on,  39,  252 
storage  (see  Storage  dams) 

Decrease    of    carrying    capacity    of 
pipes  with  age,  69 

Depth  of  canals,  46 

Design,  formulas  for  reinforced  con- 
crete, 222 

Design  of  canals,  41 


Design  of  chutes,  62 

culverts,  71 

diversion  dams,  38 

drops,  70 

flumes,  64 

headgates,  40 

irrigation  structures,  29 

pipe  lines,  65 

storage  works,  29 

turnouts,  71 

Diagrams  (see  list  page  ix) 
Dictionary  of  altitudes,  1 
Dimensions  of  metal  flumes,  249 
Discharge,  maximum,  of  streams  in 

United  States,  34 
Discharge  of  pipes,  cast-iron,  172 

concrete,  172,  174 

decrease  with  age,  69 

formulas,  69 

steel,  174 

wood  stave,  170 

Discharge  of  Cippoletti  weirs,  181 
Discharge  of  circular  conduits  flowing 

full,  151,  153 
Discharge  of  circular  conduits  flowing 

partly  full,  150,  152 
Discharge  of  rectangular  weirs,  183- 

190 
Discharge    of    rectangular    wooden 

flumes,  154-159 
Discharge     of     semicircular    flumes, 

166-169 
Discharge  of  sharp-edged  submerged 

orifices,  179 

Discharge  of  sluice  gates,  179 
Discharge  of  small  canals  in  earth, 

160-165 

Discharge  over  dams,  191,  193 
Diversion  dams, 

backwater  calculations  required, 
39 

design  of,  38 

discharge  over,  39,  191 

discussion  of,  38 

movable  crests,  38 

on  pervious  foundations,  39 

types  of,  38 

Diversion,  location  of  point  of,  24 
Drainage  basins — 

list  of,  in  United  States,  3 


INDEX 


391 


Drainage  basins,  outline  map  of,  in 
United  States,  5 

rivers  included  in  different,  3 

run  off  from,  4,  34 
Drops,  inclined,  62 

notched,  70 

vertical,  design  of,  70 
Duty  of  water,  20,  21 
Duty  of  water,  'conversion  diagram, 
196 

Elements,  hydraulic,  of  rectangular 

sections,  110-115 
of  trapezoidal  sections,   116-143 
of  circular  segments,  144-147 
of  a  horseshoe  section,  149 

Embankment  for  small  canals,  203 

Entrance  losses,  177 

Equivalents,    acre-feet   and    second- 
feet,  194 

Equivalent  units,  258 

Equivalent  water  pressure  on  retain- 
ing walls,  252 

Evaporation,  29 

Evaporation  from  reservoirs,  29 

Evaporation  tables,  30 

Examination  and  reconnoissance,  1 

Excavation  for  canals,  203-219 

Explanation  of  Figs.    4^13,  75 
"      14-20, 77 
"     21,       78 
"     22,       78 
"     23-25, 80 
"     26-29, 81 
"      30-32,  67,  82 
"     33,       82 
"      34r-35, 83 
"      36-37, 85 
"      38,       87 
"      39,       203 
"      40,        228 
"      41,        241 
"      42,        244 
"      43-45,  246 
"      46,        248 
Table  22,       79 
"      23,        81 
"     25-28, 86 
"      31-34, 206 
"      35-37, 207 


Explanation  of  Table  38,  222 
"  39-40, 228 
"  43,  240 
"  46,  241 
"  57,  261 

Fanning's    formula  for  discharge  of 

iron  pipes,  68 
Flumes,  design  of,  64 

dimensions  and  weights  of  steel, 
249 

discharge  of  steel,  166-169 

discharge  of  wooden,  154-159 
Formula  for  flow  in  canals,  50 

Kutter's,  50 

for  freeboard  on  curves,  60,  61 

for  decrease  in  carrying  capacity 
of  pipes  with  age,  69 

for  pressure  on  retaining  walls, 

220 
Formulas,  curve,  277 

for  bending  moments  in  beams, 
221 

for  canal  excavation  and  embank- 
ment, 203,  204 

for  discharge  of  pipes,  67 

for   reinforced    concrete   design, 
222 

list  of  hydraulic,  197 

trigonometric,  273 

Fractions  of  inches  expressed  in  deci- 
mals of  a  foot,  259 

Gaging  stations,  11,  13 

Gates,  discharge,  179 

General  remarks  on  canal  locations,  26 

Geological  survey,  topographic  sheets, 

1 

water-supply  papers,  2 
Grades  for  canals,  47 

Headgates,  design,  40 

discharge  through,  179 

Head    required    to    produce    veloc- 
ity, 177 

Horsepower  diagram,  253 

Horseshoe  section,  hydraulic  elements 
of,  149 

Hydraulic   curves  for   small   canals, 
160-165 


392 


INDEX 


Hydraulic  diagrams  (see  list  of  dia- 
grams, page  ix) 
Hydraulic    elements,    of   rectangular 

sections,  110-115 
of  circular  segments,  144-147 
of  a  horseshoe  section,  149 
of  trapezoidal  sections,  116-143 
Hydraulic  equivalent  units,  258 
Hydraulic  formulas,  list  of,  197 
Hydraulic   radius,    relation   to   slope 
and  velocity,  diagrams,  91-107 
Hydrostatic  formulas,  list  of,  200 

Inches    and    fractions    converted    to 

decimals  of  a  foot,  259 
Investigations  and  surveys,  20 
Irrigable  area,  determination  of,  25 

Kutter's  coefficient  «,  75,  76 
Kutter's  formula,  50 

Land,  amount  available,  1 
elevation  of,  1 
location  of,  1 

Length,  equivalent  units,  260 
Levelling,  results  of  spirit,  in  United 

States,  1 

Linear  units,  conversion  of,  260 
List  of  hydraulic  formulas,  197 
Location  of  point  of  diversion,  24 

of  main  canal,  25 

Logarithmic  diagrams,  why  used,  76 
Logarithms  of  numbers,  280 
Logs,  contents  in  feet  B.  M.,  236 
Loss  of  head  through  orifices,  sluice 

gates,  pipe  intakes,  etc.,  177 
Lumber,  contents  in  feet  B.  M.,  235 
Lyman's  tables  for  discharge  of  rec- 
tangular weirs,  184 

Materials  required  for  one  cubic  yard 

of  concrete,  232 
Materials,  weights  of,  257 
Maximum  rate  of  discharge  of  streams 

in  the  United  States,  34 
Metal  flumes,  dimensions  and  weights, 

249 

discharge  of,  166-169 
Metric  conversion  tables,  262-264 


Multipliers  for  discharge  of  broad- 
crested  weirs  and  dams,  191- 
193 

Natural  sines  and  cosines,  282 
Natural  tangents  and  cotangents,  284 
Numbers,  logarithms  of,  280 
squares,  cubes,  etc.,  292 
three-halves,  powers  of,  286 
Numbers  of  water-supply  papers,  2 

Orifices,  discharge  of  submerged,  179 
loss  of  head  through,  177 

Outlet  works  for  storage  dams,  gates 

for,  37 

location  of,  33 
velocities  through,  38 

Pipe  lines,  discussion  of,  65 

design  of,  65 
Pipes,  air  in,  69 

concrete,  steel,  cast  iron,  wood,  65 
decrease    of    carrying    capacity 

with  age,  69 

discharge  of  cast-iron,  172 
discharge  of  concrete,   172,   174 
discharge  of  steel,  174 
discharge  of  wood  stave,  170 
formulas  for  discharge  of,  67 
maximum  curvature  of  wood,  242 
spacing  of  bands  on  wood  stave, 

237,  243 
spacing  of  reinforcement  bars  in 

concrete,  237,  243 
table  of  discharge  by  Fanning's 

formula,  68 
thickness    and    weight    of    cast 

iron,  247 

thickness  and  weight  of  steel,  245 

thickness  of  staves  of  wood,  242 

Pressure    of    water    in    pounds    per 

square  inch,  250 
Pressure    of    water    in    pounds    per 

square  foot,  251 
Pressure  on  dams,  39,  252 
Precipitation,  tables  of,  6-12 
Prior  water  rights,  19 

Quantity  of  materials  required  for 
concrete,  232 


INDEX 


393 


Rain  gage,  8,  9 
Reciprocals  of  numbers,  292 
Reconnoissance,  1 

Rectangular    sections,    hydraulic    el- 
ements of,   110-115 
Rectangular   weirs,    Bazin's   formula 

and  tables  for,  189 
diagram  giving  discharge  of,  183 
discharge  of,  183-190 
Francis  formula,  183 
Lyman's  tables  of  discharge  of, 

184 
Reinforced  concrete  beams, 

coefficients  of  resistance,  229 
spacing  of  rods  in,  230,  231 
Reinforced  concrete  design,  222 
Reinforced  concrete  pipe,  spacing  of 

rods  in,  237,  243 
Reinforcement  rods  in  concrete  pipe, 

spacing  of,  237,  243 
Relative  velocities  and  slopes  for  dif- 
ferent values  of  «,  176 
Reservoir  maps,  26 
Reservoir  surveys,  26 
Reservoirs,  19 

evaporation  from,  29 
seepage  from,  32 
Retaining  walls,  220 

equivalent  water  pressure  on,  252 
Rods,  reinforcement  for  concrete  pipe, 

spacing  of,  237,  243 
Runoff  from  streams,  4 

maximum    rate    of,    streams    in 
United  States,  34 

Scouring  velocities,  48;  table,  49 
Second-feet  equivalents  in  acre-feet, 

194 

Sections,  hydraulic  elements   of  rec- 
tangular, 110-115 
of  circular,  144-147 
of  horseshoe,  149 
of  trapezoidal,' 116-143 
Seepage  losses,  43 

Seepage  losses,  diagram  for  estimat- 
ing, 45 

in  percent  of  diversion,  24 
table  of,  44 

Segments,  hydraulic  elements  of  cir- 
cular, 144-147 


Side  slopes  for  canals,  44 

Silting  velocities,  48;  table,  49 

Sines,  natural,  282 

Slope  of  open  channels,  diagrams  for 

determining,  91-107 
Sluice  gates,  coefficients  of  discharge 
of,  84,  179 

discharge  of,  179 

loss  of  head  through,  177 
Spacing  of  bands  on  wood-stave  pipe, 

237,  243 
Spacing  of  rods  in  concrete  pipe,  237, 

243 
Spacing  of  round  and  square  bars  in 

beams,  230,  231 
Specifications,  315 

Advertisement,  316 

detail  specifications,  326 

General  Conditions,  319 

Guarantee  of  Bond,  318 

Notice  to  Bidders,  317 

Proposal,  317 

Special  Conditions,  328 
Specifications  for 

Canal  Excavation,  329 

Cast  Bronze,  386 

Cast-iron  Pipe,  352 

Cement,  371 

Concrete,  366 

Continuous    Wood- Stave   Pipe, 
338 

Excavation  for  Structures,  337 

Forged  or  Rolled  Bronze,  384 

Gray-Iron  Castings,  381 

Machine  -  Banded  Wood  -  Stave 
Pipe,  342 

Malleable  Castings,  382 

Metal  Flumes,  355 

Paving,  369 

Reinforced  Concrete  Pipe,  348 

Steel  Castings,  383 

Steel  Highway  Bridges,  358 

Steel  Pipe,  345 

Steel  Reinforcement  Bars,  380 

Structural  Steel,  379 

Timber  Piles,  378 

Tunnels,  334 
Spillways,  maximum  discharge  over, 

33 
Squares  of  numbers,  292 


394 


INDEX 


Stadia  Tables,  266 

Staves  for  wood  pipe,  thickness  of,  242 

Steel  flumes,  discharge  of,  166-169 

dimensions  and  weights,  249 
Steel  pipe,  discharge  of,  174 

maximum  allowable  backfill  for, 
244 

thickness  of  shell,  245 

weight  of,  245 
Storage  dams,  outlet  works  for,  33 

spillways  for,  33 

types  of,  33 
Storage  works,  dams,  33 

design  of,  29 

discussion  of,  29 

study  of  water-supply,  29 
Structures,  design  of,  29 
Submerged  orifices,  discharge  of,  179 
Submerged  tubes,  coefficients  of  dis- 
charge for,  84 

Submerged  weirs,  coefficients  for  dis- 
charge, 180 
Surveys,  20 
Surveys  for  reservoirs,  26 

Tables  (see  list  page  xi) 

Tangents,  natural,  284 

Theoretical     horse-power    of    falling 

water,  253 

Theoretical  velocity  head,  177 
Thickness  of  cast-iron  pipe,  247 
Thickness  of  staves  for  wood  pipe,  242 
Thickness  of  steel  pipe,  245 
Three-halves  powers  of  numbers,  286 
Timber,  allowable  stresses  in,  233 

weights  of,  233 
Timber  structures,  232 
Topographic  sheets  of  United  States 

Geological  Survey,  1 
Total  hydrostatic  pressure  on  walls, 

252 

Trapezoidal  loading  on  beams,  221 
Trapezoidal   sections,   hydraulic   ele- 
ments of,  116-143 
Triangular   loading   on   beams,   221, 

table,  223 

Trigonometric  formulas,  273 
Tubes,  discharge  coefficient  for  sub- 
merged, 84 
Turnouts,  design  of,  71 


Uniform  loading  on  beams,  221 

Value  of  Kutter's   coefficient   n,  50, 
75,  176;  tables,  52 

Values  of  coefficient  "C"  for  open 
channels,  90-109 

Variation  of  velocity  and  slope  with 
n,  176 

Velocities,  in  canals,  47 ;  diagrams  for 

determining,  91-107 
scouring  and  silting,  48;  table,  49 

Velocity  head,  177 

Velocity  of  approach  to  weirs,  coef- 
ficients for,  182 

Vertical  drops,  70 

Volume,  equivalent  units  of,  258 

Volume  of  excavation  and  embank- 
ment for  small  canals,  205 

Volume  of  excavation  for  canals  in 
level  ground,  206,  208-213 

Volume  of  excavation  for  canals  in 
sloping  ground,  207,  214-219 

Walls,  hydrostatic  pressure  on,  252 
Water,  horse-power  produced  by  fall- 
ing, 253 

maximum  requirement  for,  23 
quantity  applied  to  land,  20 
used  on  projects  of  the  U.  S.  Re- 
clamation Service,  21 
variation  of  use  through  season, 

22,23 

Water  duty,  20,  21 
Water  duty,  conversion  diagram,  196 
Water  pressure  in  pounds  per  square 

foot,  251 
Water  pressure  in  pounds  per  square 

inch,  250 

Water  rights,  prior,  19 
Water  supply,  papers  published  by  U. 

S.  Geological  Survey,  2 
quantity,  1 
source  of,,l 

Weight  of  cast-iron  pipe,  247 
metal  flumes,  249 
round  and  square  rods,  230,  231 
steel  pipe,  245 
timber,  233 
various  substances,  257 


INDEX  395 

Weirs,   broad-crested,    discharge   of,  Weir  station,  gage  readings  at,  8 

191-193  Wooden  beams,  values  of  M  /S  for,  234 

Cippoletti,  discharge  of,  181  Wooden  columns,  formula  for,  233 

coefficients  for  submerged,  180  Wooden  flumes,  discharge  of,  154-159 

coefficients   for  velocity  of  ap-  Wood-stave  pipe,  discharge,  170 
proach,  182  maximum  curvature  for,  242 

discussion  of,  11  size  of  wire  used  for  banding,  244 

rectangular,   discharge  of,    183-  spacing  of  bands  on,  237,  243 

190  thickness  of  staves,  242 


OV  *'-°°    O        THE    S^M*™ 

DAY 


•7/33 


312523 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


